| THURSDAY Jan. 19 : | Faculty Meeting |
| Title: | Faculty Meeting |
| . | |
| Time and Place: | 2:30 PM CW 122 |
| TUESDAY Jan. 24 : | TWENTY-THIRD ISIDORE & HILDA DRESSLER LECTURE |
| Title: | Adding and Counting |
| Ken Ono
Emory University Abstract: In mathematics, the stuff of partitions seems like mere child's play. The speaker will explain how the simple task of adding and counting has fascinated many of the world's leading mathematicians: Euler, Ramanujan, Hardy, Rademacher, Dyson, to name a few. And as is typical in number theory, many of the most fundamental (and simple to state) questions have remained open. In 2010, the speaker, with the support of the American Institute for Mathematics and the National Science Foundation, assembled an international team of distinguished researchers to attack some of these problems. Come hear Professor Ono speak about their findings: new theories which solve some of the famous old questions. | |
| Time and Place: | 2:30 PM CW 102 |
| Number Theory Seminar | |
| Title: | The legacy of Ramanujan's mock theta functions: Harmonic Maass forms in number theory |
| Ken Ono
Emory University In his last letter to G. H. Hardy (written from his death bed in 1920), Ramanujan wrote about a new beautiful theory of power series that he refers to as "mock theta functions". This small collection of enigmatic power series puzzled mathematicians for many decades. Then in 2002 Zwegers realized the meaning behind these series; he established that these series are pieces of Maass forms. This understanding has inspired much work. The development of general theorems based on Ramanujan's examples has produced many wonderful theorems on a wide array of subjects such as: L-functions and elliptic curves, Additive number theory (partitions), Donaldson invariants, Representation theory, Explicit class field theory. This talk will be a brief account of this story. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| WEDNESDAY Jan. 25 : | Analysis Seminar |
| Title: | The Pompeiu Problem |
| A. G. Ramm,
Kansas State University The Pompeiu Problem A.G. Ramm Department of Mathematics Kansas State University, Manhattan, KS 66506-2602, USA ramm@math.ksu.edu; http://www.math.ksu.edu/ ramm Abstract Let f(x) be a locally integrable function in R^n, n \geq 2, and let D be a bounded domain in R^n , homeomorphic to a ball. Assume that the boundary S of D is sufficiently smooth, S\in C^a , a > 1 is sufficient. Suppose that the integral of f(x) over D and over the domains obtained from D by all rigid motions, (that is, by all translations and rotations) vanishes: \int_D f (gx + y)dx = 0 for every y in R^n and every g,where g is an arbitrary rotation of the coordinate system. Does this imply that f(x)= 0? If yes, then we say that the domain D has P-property. This question was raised in 1929 by D.Pompeiu who gave a positive answer. This answer turned to be wrong: some balls do not have P-property. Presently the Pompeiu problem (P-problem), can be stated as follows: Is it true that the ball is the only bounded domain homeomorphic to a ball that fails to have P-property? This problem will be discussed and reduced to a symmetry problem for a PDE. Some problems, the solution of which will yield the solution to P-problem, will be formulated. Bibliography [1] A. G. Ramm, The Pompeiu problem, Applicable Analysis, 64, N1-2, (1997), 19-26. [2] A. G. Ramm, Necessary and sufficient condition for a domain, which fails to have Pompeiu property, to be a ball, Journ. of Inverse and Ill-Posed Probl., 6, N2, (1998), 165-171. [3] A. G. Ramm, A symmetry problem, Ann. Polon. Math., 92, (2007), 49-54. [4] A. G. Ramm, Symmetry problem, Proc. Amer. Math. Soc., (2012) (to appear) [5] N.S.Hoang and A. G. Ramm, Symmetry problems 2, Annal. Polon. Math., 96, N1, (2009),61-64. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| MONDAY Jan. 30 : | Algebra Seminar |
| Title: | An introduction to higher algebraic K-theory |
| Eric Bunch
Kansas State University AbstractThis talk is the first in a series of two talks. In it, I will give a short introduction to two higher algebraic K-theories. The first will be as defined by Daniel Quillen in his famous 1973 paper, via homotopy groups of the classifying topological space of a category associated with a given exact category (so called, Q-construction). The second theory is the 'universal' higher K-theory, due to Alexander Rosenberg. It is purely algebraic and obtained as an application of general machinery of non-additive homological algebra. In the case of abelian categories, there exists a canonical homomorphism from Quillen's K-theory to the universal K-theory. The talk concludes with posing the question if this morphism is an isomorphism, i.e. If both theories are the same for abelian categories. The answer to this question will be the subject of the second talk. | |
| Time and Place: | 4:30 PM CW 146 |
| WEDNESDAY Feb. 01 : | Analysis Seminar |
| Title: | Fourier series acceleration and Hardy-Littlewood series |
| Chuck Moore,
Kansas State University I will discuss some sequence acceleration methods and their effects on Fourier series. An interesting example in this study is provided by certain series investigated by Hardy and Littlewood. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Feb. 02 : | Faculty Meeting |
| Title: | Faculty Meeting |
| . | |
| Time and Place: | 2:30 PM CW 122 |
| Function Theory Study Seminar | |
| Title: | Rigidity Theorems in Geometric Function Theory. |
| Hrant Hakobyan
Kansas State University Abstract: An old theorem of Koebe states that any finitely connected domain of the plane can be mapped conformally onto a circle domain (i.e. one bounded by circles and points). We will start by showing rigidity of circle domains and will continue by describing some of the more recent results on quasisymmetric rigidity of Schottky sets and Sierpinski carpets of Bonk, Kleiner and Merenkov. These results may be found in the following papers. http://front.math.ucdavis.edu/1102.4381 http://front.math.ucdavis.edu/1102.3224 http://www.math.uiuc.edu/~merenkov/papers/rlsfinal.pdf | |
| Time and Place: | 3:30 PM CW 143 |
| MONDAY Feb. 06 : | Topology Seminar |
| Title: | Manifold calculus of functors |
| Victor Turchin
Kansas State University Abstract: In the talk I will give an overview of a theory developed by Goodwillie and Weiss in order to study spaces of embeddings of one manifold into another. In two words the idea is to break the source manifold into smaller pieces and try to patch the information together. For the fans of abstract nonsense I will tell that the obtained approximation spaces are actually homotopy sheafifications with respect to certain Grothendieck topologies. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | An introduction to higher algebraic K-theory II |
| Eric Bunch
Kansas State University AbstractThis talk is the first in a series of two talks. In it, I will give a short introduction to two higher algebraic K-theories. The first will be as defined by Daniel Quillen in his famous 1973 paper, via homotopy groups of the classifying topological space of a category associated with a given exact category (so called, Q-construction). The second theory is the 'universal' higher K-theory, due to Alexander Rosenberg. It is purely algebraic and obtained as an application of general machinery of non-additive homological algebra. In the case of abelian categories, there exists a canonical homomorphism from Quillen's K-theory to the universal K-theory. The talk concludes with posing the question if this morphism is an isomorphism, i.e. If both theories are the same for abelian categories. The answer to this question will be the subject of the second talk. | |
| Time and Place: | 4:30 PM CW 146 |
| TUESDAY Feb. 07 : | M-Seminar |
| Title: | Symplectic Cohomology and the Hochschild (co)homology of the Fukaya category |
| Sheel Ganatra,
University of California, Berkeley Abstract: Let M be an exact symplectic manifold. Under non-degeneracy assumption implying the existence of enough Lagrangians, we show that the symplectic cohomology of M is isomorphic to both the Hochschild cohomology and Hochschild homology (with a shift) of M's wrapped Fukaya category. The relevant ingredients are: Fourier-Mukai theory for the wrapped Fukaya category via holomorphic quilts, a version of the Cardy condition, and a new self-duality for the wrapped Fukaya category (a non-compact version of the Calabi-Yau condition). | |
| Time and Place: | 3:30 PM CW 120 |
| WEDNESDAY Feb. 08 : | Analysis Seminar |
| Title: | Spectral measure for a self-adjoint operator via the heat semigroup |
| Frederic Bernicot,
Laboratoire de Mathematiques Jean Leray, Nantes, France We aim to describe how we can encode the spectral measure associated to a self-adjoint operator using only the heat semigroup (with complex time). As an application, we will then see how dispersive estimates imply restriction inequality (boundedness of the spectral measure), recovering some existing results. Moreover a general smoothing effect for the corresponding Schrodinger equation can be obtained and will be described. | |
| Time and Place: | 4:30 PM CW 122 |
| THURSDAY Feb. 09 : | Function Theory Study Seminar |
| Title: | Quasisymmetric rigidity of Schottky sets |
| Hrant Hakobyan
Kansas State University A subset S of R^n is called a Schottky set if its complement consists of mutually disjoint balls. We will go over some recent papers of Merenkov and others about QS rigidity of such sets. | |
| Time and Place: | 3:30 PM CW143 |
| Mathematics Education Seminar | |
| Title: | Mining Diagnostic Assessment Data |
| Andrew Bennett
Kansas State University Diagnostic assessments are used to identify misconceptions and areas of weakness that should be remediated for students as they move into more advanced material. One issue is that students often come up with innovative ways to make mistakes that are not anticipated by the designer of the instrument. This talk will discuss a "gray box" data mining approach to cluster concepts to understand such inventive responses in the context of previously identified concepts. It can also be used to compute a "distance" between concepts which may help the instructor visualize the relative difficulty of concepts for the students in the class. | |
| Time and Place: | 4:30 PM CW 122 |
| MONDAY Feb. 13 : | Algebra Seminar |
| Title: | The Hochschild cohomology of pasting diagrams, II |
| David Yetter
Kansas State University The Hochschild cochain complexes of k-linear categories and (parallel pairs of) k-linear functors assembles by iterated cone constructions to give cochain complexes the cohomology of which classifies deformations of pasting diagrams of k-linear categories, thereby extending results of Gerstenhaber and Schack on diagrams of algebras. If time permits we will describe a method of Shrestha by which the standard result that obstructions are cocycles is proved in the case of particular pasting diagrams, and indicate a program to prove the result in general. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | Realization of regular function algebras as cohomology rings of quantum groups at roots of unit. |
| Zongzhu Lin
Kansas State University Abstract It is known that the algebra of regular functions on the nilpotent variety (nullcone) of a semi-simple Lie algebra in positive characteristics (which are not too small) are even degree part of the restricted Lie algebra cohomology ring of the corresponding Lie algebra and therefore provides a realization of the cohomological support varieties of representations of restricted Lie algebras in terms of the geometry of the nilpotent variety. Over the field of complex numbers, Ginzburg and Kumar proved an analogy result that the algebra of regular functions of the nullcone of a semisimple Lie algebra is the cohomology ring of the small quantum group at roots of unity (with degree larger than the coxeter number), which was used later to establish connections between the trivial block of the category of representations of quantum groups at roots of unity and category of perverse sheaves of affine grassmannian through the geometry of nullcone and the springer resolution. This talk will be focusing on other Richardson nilpotent orbit closures, which corresponds to parabolic subgroups with a hope to establish connections between singular blocks of representations of quantum groups with geometry of cotangent bundles of generalized flag varieties. | |
| Time and Place: | 4:30 PM CW146 |
| WEDNESDAY Feb. 15 : | Analysis Seminar |
| Title: | Strong solutions to an elliptic obstacle problem with coefficients in VMO |
| Kubrom Teka,
Kansas State University We consider the obstacle problem: $$a^{ij}D_{ij}w = \Chi_{w> 0} in B_1 \ \ \ \text{with} \ \ \ w = \psi \ \text{on} \ \partial B_1$$ where we assume that the coefficients $a^{ij}$ belong to VMO, that the functions $w, \psi \geq 0$ belong to the Sobolev space $W^{2,p},$ and that $w$ satisfies the PDE pointwise almost everywhere. We show existence, uniqueness, regularity, and nondegeneracy of the solutions. These results allow us to begin the study of the regularity of the free boundary. In particular, we establish a measure theoretic version of the Caffarelli Alternative after showing a measure stability result for the contact sets. (This is a joint work with Ivan Blank.) | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Feb. 16 : | M-Seminar |
| Title: | On Lagrangian spheres, sheaves and mirror symmetry of open Calabi-Yau's |
| Diego Matessi,
University of Milan Abstract: I will describe a precise conjecture on the homological mirror symmetry of A_n singularities in dimension 3. To support this conjecture, I will discuss some results on the topology of Lagrangian sections and vanishing cycles via Lagrangian fibrations. Although the main motivation is to understand A_n singularities, the methods apply to more general open Calabi-Yau manifolds and seem to promise various generalizations. This is work in progress with Mark Gross. | |
| Time and Place: | 3:30 PM CW 146 |
| (notice non-standard meeting day) | |
| Function Theory Study Seminar | |
| Title: | Quasisymmetric rigidity of Schottky sets II |
| Hrant Hakobyan,
Kansas State University Abstract A subset S of R^n is called a Schottky set if its complement consists of mutually disjoint balls. We will go over some recent papers of Merenkov and others about QS rigidity of such sets. | |
| Time and Place: | 3:30 PM CW 143 |
| Mathematics Education Seminar | |
| Title: | Mathematical Knowledge for Teaching Undergraduates |
| Carlos Castillo-Garsow
Kansas State University In 1986, Shulman published an article that introduced many to the idea of pedogicial content knowledge (PCK): Content knoweldge that is rarely needed in contexts outside of teaching. Later, Ball et. al. (2008) refined this idea for mathematics and developed a taxonomy of mathematical knowledge for teaching (MKT): The mathematical knowledge that is necessary for successful teaching, including general mathematical content knowledge and differnt types of PCK. Studies in mathematical knowledge for teaching have primarily focused on primary and secondary teachers, and a criticism of these studies is that because teacher's mathematical content knowledge can be poor, it is difficult to separate difficulties based on general content knowledge and pedagogical content knowlege. In 2012 Johnson and Larsen answered this criticism by investigating the role of PCK in teaching undergraduate mathematics. In order to better study the differences in types of MKT, they studied a professional mathematician teaching an abstract algebra course. This paper describes both the PCK related difficulties that the instructor had in teaching the course as well as the advantages that professional level mathematical skill brings to developing PCK. In this talk, the results of Johnson and Larsen will be contrasted with a classic study of a middle school teacher (Thompson & Thompson, 1994) in order to highlight the importance of PCK and the effect of mathematical skill in developing PCK. | |
| Time and Place: | 4:30 PM CW 122 |
| MONDAY Feb. 20 : | Topology seminar |
| Title: | Optical black holes |
| Shawn Westmoreland
Kansas State University Abstract: A notion of spacetime geometry can be derived from a physical field - in our case, a conformal geometry can be derived from the electromagnetic field. This idea was developed most extensively by the Brazilian physicist Mario Novello. The Lagrangian for the classical field theory of electromagnetism can be modified in order to approximate quantum effects - i.e. the scattering of light by light. This modified Lagrangian leads to the so-called Euler-Heisenberg field equations. We can solve the Euler-Heisenberg field equations for a uniform current running through an infinite wire, immersed in a constant electric field directed along the wire. Provided that the fields are sufficiently intense, we can show that the space-time geometry corresponds to a cylindrically symmetric optical black hole when the Poynting vector points inwards (or a white hole when the Poynting vector points outwards). This work was the subject of my Phd thesis, completed under Louis Crane. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | Models, Morphisms, and Exotica |
| Andrew Chermak
Kansas State University This lecture will introduce saturated fusion systems on finite p-groups, as "sheaves of local groups", in which the stalk at a point P is a finite group M_P in which P is a normal p-subgroup, and having the property that the centralizer C_M(P) of P is contained in P. I'll discuss the questions: (1) Do the stalks assemble, in some useful sense, into a model for the whole saturated fusion system ? (Answer: "Yes", but while the model is a finite set with multiplication and inversion, it needn't be a group. It's what's called a "locality".) (2) What is the "right notion" of morphism of localities ? (3) Can one dream realistically, and at the same time deliriously, of using localities to unlock some basic mysteries concerning the classification of the finite simple groups ? | |
| Time and Place: | 4:30 PM CW 146 |
| TUESDAY Feb. 21 : | Seminar |
| Title: | Operator Algebras Seminar |
| Sarah Reznikoff
This will be the first in a series of lectures concerning the interaction between operator algebras and set theory. We'll start with a statement of Naimark's Problem and present a rough presentation of the set theory background necessary to understand and appreciate the Akemann-Weaver counterexample in ZFC + [Diamond]. | |
| Time and Place: | 1:00 PM 204 Burt Hall |
| TWENTY-THIRD HARRY E. VALENTINE LECTURE | |
| Title: | What is Mirror Symmetry in String Theory? |
| Lev Borisov
Rutgers University Abstract: String theory attempts to describe the physical world by expressing fundamental forces and forms of matter in terms of tiny vibrating one-dimensional objects (strings) in place of usual points in space. While string theory is yet to be tested experimentally, it has considerable inner beauty and has spawned a number of fascinating mathematical developments. Mirror Symmetry is one such mathematical offshoot, and is the primary object of study at the M-center at Kansas State University. I will give an overview of the subject and its history for the general audience. | |
| Time and Place: | 2:30 PM CW 102 |
| M-Seminar | |
| Title: | Vertex algebra approach to mirror symmetry |
| Lev Borisov,
Rutgers University Abstract: I will review the vertex algebra approach to mirror symmetry, including recent developments such as unification of Batyrev-Borisov and Berglund-Hubsch toric examples. | |
| Time and Place: | 3:30 PM CW 120 |
| WEDNESDAY Feb. 22 : | Analysis seminar |
| Title: | Laws of the iterated logarithm for general lacunary series |
| Xiaojing Zhang,
Kansas State University Suppose f(x) is defined on R^n and n_k is a lacunary sequence. We consider sums of functions of the form a_k f(n_k x), where a_k is real. With minimal hypotheses on f, we show that these sums satisfy a law of the iterated logarithm. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Feb. 23 : | SEVENTH BRENT P. SMITH MEMORIAL LECTURE |
| Title: | Fractional Brownian Motion: Stochastic Calculus and Applications |
| David Nualart
University of Kansas Abstract: The fractional Brownian motion is a centered, self-similar Gaussian process with stationary increments, which depends on a parameter H in (0,1) called the Hurst index. In this talk we will first describe some basic properties of the fractional Brownian motion, such as long-range dependence and finite p-variation. The fractional Brownian motion can be regarded as a fractional derivative of the classical Brownian motion. We will introduce a general class of stochastic processes related to the fractional Brownian motion, called fractional semimartingales, and we will discuss the p-variation of their trajectories. The applications of the fractional Brownian motion to model data coming from engineering, finance and other areas, require the construction of a suitable stochastic calculus, similar to the classical Ito calculus. We will present several approaches to the stochastic calculus with respect to the fractional Brownian motion using path-wise techniques, Riemann sums and Malliavin calculus. | |
| Time and Place: | 2:30 PM TH 1018 |
| Function Theory Study Seminar | |
| Title: | "Quasisymmetric rigidity of square Sierpinski carpets" by Bonk and Merenkov |
| Pietro Poggi-Corradini
Kansas State University Abstract: I am a virtual god-father for this paper. I saw it being born and I followed through its first baby steps. I will try to retell its story by reading the recent preprint that was posted on Arxiv. | |
| Time and Place: | 3:30 PM CW 143 |
| MONDAY Feb. 27 : | Topology seminar |
| Title: | McKay correspondence |
| Louis Crane
Kansas State University Abstract: This talk is the first of three that Louis Crane is planning to deliver this semester. It will begin with elementary material related to the platonic solids and give a non-technical introduction to the classification of lie algebras. We then will explore the connection between them called the Mckay correspondence, and learn various ways to understand it. Later talks will explore physical applications, and will include an exposition of vertex operators. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | Fixed Point Sets and Lefschetz Modules for Subgroup Complexes |
| John Maginnis
Kansas State University Abstract (joint work with Silvia Onofrei) If a finite group acts on a finite simplicial complex, the virtual Lefschetz module is constructed as the alternating sum of the chain complex. The best known example is the Steinberg module for a finite group of Lie type acting on its Tits building, a module which is irreducible and projective. Another important example is the Brown complex for any finite group (simplices are chains of p-subgroups) yielding a projective (but not necessarily irreducible) virtual Lefschetz module. This result is proven using the fact that certain fixed point sets are contractible. Dr. Onofrei and I study another subgroup complex, using p-subgroups which contain in their center an element lying in the center of a Sylow p-subgroup. We have theorems concerning the homotopy type of certain fixed point sets, and determine information about indecomposable summands of the Lefschetz module (vertices and defect groups of their blocks). | |
| Time and Place: | 4:30 PM CW 146 |
| TUESDAY Feb. 28 : | Operator Algebras Seminar |
| Title: | Set theory background: independence proofs and forcing |
| Sarah Reznikoff
Kansas State University We will continue our preparation for examining the overlap between set theory and C*-algebras. In particular, we will go over the basics of independence proofs and provide an introduction to forcing. | |
| Time and Place: | 1:00 PM 204 Burt Hall |
| M-Seminar | |
| Title: | Plane curve singularities, Hilbert schemes, HOMFLY homology, and Cherednik algebras |
| Vivek Shende,
M.I.T. Abstract: I will discuss a conjecture identifying the cohomology of certain nested Hilbert schemes of points on a plane curve singularity with the HOMFLY homology of the link of that singularity. The conjecture may be restated in terms of the cohomology of parabolic Hitchin fibers, in which form, and when restricted to toric singularities, it suggests the existence of the action of a rational Cherednik algebra on the HOMFLY homology of torus knots. As a consequence, the conjectures predict that the homology of (n,n+1) torus knots is described by formulas familiar from Haiman's study of diagonal harmonics, and the (n,mn+1) torus knots by known generalizations of these. | |
| Time and Place: | 3:30 PM CW 120 |
| WEDNESDAY Feb. 29 : | Analysis Seminar |
| Title: | Quasiconformal Geometry of Slit Carpets |
| Hrant Hakobyan
Kansas State University Abstract: We study a class of spaces homeomorphic to the Sierpinski carpet - slit carpets. These carpets are all Ahlfors 2-regular metric measure spaces (so of Hausdorff dimension 2) and have no manifold points. We show that if S is a slit carpet the the following are equivalent: - S can be quasisymmetrically embedded into the plane, - S is a Loewner space in the sense of Heinonen and Koskela, - S satisfies a (1,p)-Poincare inequality for every p>1, or equivalently for some p>1. Carpets, which do not embed into the plane are quasisymmetrically equivalent if and only if they are isometric. Carpets, which embed into the plane can be embedded as round Sierpinski carpets of positive measure. | |
| Time and Place: | 4:30 PM CW122 |
| Analysis Seminar | |
| Title: | Quasisymmetric Geometry of Slit Carpets |
| Hrant Hakobyan,
Kansas State University We study a class of spaces homeomorphic to the Sierpinski carpet - slit carpets. These carpets are all Ahlfors 2-regular metric measure spaces (so of Hausdorff dimension 2) and have no manifold points. In particular we show that if S is a slit carpet then the following are equivalent: * S can be quasisymmetrically embedded into the plane, * S is a Loewner space in the sense of Heinonen and Koskela, * S satisfies a (1,p)-Poincare inequality for every p>1, or equivalently for some p>1. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Mar. 01 : | Function Theory Study Seminar |
| Title: | "Quasisymmetric rigidity of square Sierpinski carpets" by Bonk and Merenkov (cont.) |
| Pietro Poggi-Corradini
Kansas State University Abstract: I am a virtual god-father for this paper. I saw it being born and I followed through its first baby steps. I will try to retell its story by reading the recent preprint that was posted on Arxiv. | |
| Time and Place: | 3:30 PM CW 143 |
| Mathematics Education Seminar | |
| Title: | Pre-service elementary teachers' ability and understanding in proof |
| Carlos Castillo-Garsow
Kansas State University Stylianides and Stylianides engaged in a four year design experment target at improving elementary teacher's understanding of proof. In the last cycle of the design experiment, the researchers worked with 39 pre-service elementary teachers on proof and developing critera for proof. Through the use of both coding and cases, the authors make the case that ability to prove does not necessarily reflect understanding of proof. | |
| Time and Place: | 4:30 PM CW 122 |
| MONDAY Mar. 05 : | Topology seminar |
| Title: | Homotopy Calculus of Functors |
| Victor Turchin
Kansas State University Abstract: This is an introductory talk on the Calculus of Functors that studies functors from the category of topological spaces or spectra to topological spaces or spectra. This theory was started by T. Goodwillie and later showed to have a lot of applications in particular in the study of homotopy groups. The talk will help to better understand the colloquium lecture by N. Kuhn that will be given on Thursday of the same week. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | Canonical Basis and Crystal Basis |
| Zongzhu Lin
Kansas State University AbstractAbstract: This is an introductory talk on canonical basis and crystal basis. In 1989, Lusztig constructed canonical basis of quantized enveloping algebras. At Kashiware also constructed crystal basis (q=0 case). In the first talk, I will outline Lusztig's construction of canonical basis. Hopefully, in the future I talk about Kashiware's Crystal basis and later global crystal basis as well as applications of the canonical basis in representation in representation theory and combinatorics, in particular their relations with Kazhdan-Lusztig theory on decomposition numbers of standard representations for Heck algebras, Schur algebras, quantum groups) | |
| Time and Place: | 4:30 PM CW 146 |
| TUESDAY Mar. 06 : | Operator Algebras Seminar |
| Title: | Set theory background: independence proofs and forcing |
| Sarah Reznikoff
Kansas State University We continue, today introducing forcing. | |
| Time and Place: | 1:00 PM 204 Burt Hall |
| Faculty Meeting | |
| Title: | Faculty Meeting |
| . | |
| Time and Place: | 2:30 PM CW 122 |
| M-Seminar | |
| Title: | Mukai-type flops via D-modules |
| Rina Anno,
University of Massachusetts, Amherst Abstract: This talk is based on a joint work in progress with Ivan Mirkovic. Flops are a special class of birational maps between algebraic varieties. It is expected that when two varieties are related by a flop, their derived categories of coherent sheaves are equivalent. However, it was shown by Namikawa in 2002 that even in the low-dimensional case of the so-called Mukai flop between two copies of $T^*P^2$ the functor immediately associated to the flop is not an equivalence, and while the equivalence still exists, it is given by a different functor. It turns out that if we switch to the world of D-modules then both of these functors can be explained quite naturally, and equivalences can be produced for a wide class of similar flops between $T^*X$, where $X$ are Grassmannians and other partial flag varieties. | |
| Time and Place: | 3:30 PM CW 120 |
| WEDNESDAY Mar. 07 : | Analysis Seminar |
| Title: | Sobolev inequalities modeled by convex functions |
| Diego Maldonado
Kansas State University Abstract: We prove Sobolev inequalities in a doubling quasi-metric space context where the measure and the geometry are determined by convex functions. The results apply to second-order degenerate elliptic operators. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Mar. 08 : | FORTY-FIFTH WILLIAM J. SPENCER LECTURE |
| Title: | Polynomial Functors in Homotopy Theory |
| Nicholas Kuhn
University of Virginia Abstract: The calculation of the homotopy groups of a topological space is notoriously difficult. By contrast, homology groups are much easier to calculate because they satisfy the nice Meyer-Vietoris decomposition rule. Said diff erently, homology groups are the homotopy groups of a linear functor from spaces to spaces. We discuss what this means and how this can be generalized to the notion of a polynomial functor. A general functor has a best approximation by a polynomial functor of degree n, with nth Taylor coefficient a geometric object with an action of the nth symmetric group. When applied to the identity functor, and then specialized to spheres, many miracles happen, that give a conceptual explanation for a number of aspects of the homotopy groups of spheres. | |
| Time and Place: | 2:30 PM TH 1018 |
| Function Theory Study Seminar | |
| Title: | Smoothness and restrictions of functions |
| Diego Maldonado
Kansas State University Abstract: What does it mean for a function to have 6.329 derivatives? Why does an a.e. differentiable function f:R^3 -> R lose "half of a derivative" when restricted to a plane? Why does the restriction make sense at all (since a plane has measure zero in R^3)? How can averages of a function imply its differentiability? These and other highly intriguing questions are to be happily addressed. Graduate students are strongly encouraged to attend. | |
| Time and Place: | 3:30 PM CW 143 |
| Topology seminar | |
| Title: | A topological non-realization theorem |
| Nicholas Kuhn
University of Virginia Abstract: The mod p cohomology of a topological space is a module over the Steenrod algebra A of Steenrod reduced power operations. We discuss a non-realization theorem, which informally says that the cohomology of a space must be either very small or very large: Theorem If an A–module is finitely generated as an A–module, but is infinite dimensional as a Z/p–vector space, then it can not be realized as the reduced cohomology of a topological space. This was conjectured, and partially proved, by the speaker in the mid 1990’s. Quite recently the proof has been completed by Lionel Schwartz and Gerald Gaudens. The organizing principle for all of us is to use algebraic properties of the category of unstable A–modules and work on the Sullivan conjecture by Lannes and others. | |
| Time and Place: | 4:30 PM CW 131 |
| Mathematics Education Seminar | |
| Title: | Automated textual analysis of word problems |
| Andrew Bennett
Kansas State University While automated homework systems can generate large numbers of problems from a standard template by varying parameters and/or functions, generating random word problems is a more difficult task. Cetintas et. al. used support vector machines (SVMs) to classify sentences in student generated word problems as relevant or irrelevant. Their goal was to develop an automated method to define the amount of “noise” in a word problem to allow an online system to mine an increasing database of student generated problems to pick problems of a desired complexity. In this talk I will give an overview of the SVM approach for generating classification rules and how it was used here in analyzing textual data. This talk will be a little more mathematically dense than previous talks in this seminar. | |
| Time and Place: | 4:30 PM CW 122 |
| MONDAY Mar. 12 : | Topology seminar |
| Title: | Particle Physics from a Mathematical Perspective |
| Louis Crane
Kansas State University Abstract: Recent developments in neutrino physics have changed the picture of particle physics in an interesting way. Each generation has 16 fermions instead of 15, and we mathematicians know how different those numbers are. I will present a self contained description of the new picture, and point out the mathematical implications. The talk is one of a series outlining a new approach to the construction of a unified field theory based on the quantum Mckay corrspondence, connecting module categories and vertex operators in the old dual model. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | Canonical Basis and Crystal Basis II |
| Zongzhu Lin
Kansas State University (Part II) This is an introductory talk on canonical basis and crystal basis. In 1989, Lusztig constructed canonical basis of quantized enveloping algebras. At Kashiware also constructed crystal basis (q=0 case). In the first talk, I will outline Lusztig's construction of canonical basis. Hopefully, in the future I talk about Kashiware's Crystal basis and later global crystal basis as well as applications of the canonical basis in representation in representation theory and combinatorics, in particular their relations with Kazhdan-Lusztig theory on decomposition numbers of standard representations for Heck algebras, Schur algebras, quantum groups) | |
| Time and Place: | 4:30 PM CW 146 |
| THURSDAY Mar. 15 : | FORTY-SIXTH WILLIAM J. SPENCER LECTURE |
| Title: | SYZ Transformation In Mirror Symmetry |
| Naichung Conan Leung
Institute for Mathematical Sciences/Chinese University of Hong Kong Abstract: Mirror symmetry is a duality between complex geometry and symplectic geometry. In this talk I will explain the Strominger-Yau-Zaslow proposal which explains mirror symmetry via Fourier type transformation along Lagrangian fibrations. I will also discuss recent progress on the SYZ proposal. | |
| Time and Place: | 2:30 PM TH 1018 |
| Function Theory Study Seminar | |
| Title: | Smoothness and restrictions of functions (cont.) |
| Diego Maldonado
Kansas State University Abstract: What does it mean for a function to have 6.329 derivatives? Why does an a.e. differentiable function f:R^3 -> R lose "half of a derivative" when restricted to a plane? Why does the restriction make sense at all (since a plane has measure zero in R^3)? How can averages of a function imply its differentiability? These and other highly intriguing questions are to be happily addressed. Graduate students are strongly encouraged to attend. | |
| Time and Place: | 3:30 PM CW 143 |
| MONDAY Mar. 26 : | Topology seminar |
| Title: | The quantum Mckay correspondence and quantum field theory |
| Louis Crane
KSU Abstract: The construction of Frenkel Jing and Wang explains the Mckay correspondence. I will explain that it is a quantum field theory, and give an introduction to vertex operators. In my next talk, I will show how to couple this to a state sum model of quantum gravity, and explain why it begins to look like a unified field theory. | |
| Time and Place: | 3:30 PM CW 120 |
| Lecture for graduate students | |
| Title: | Cluster recursions |
| Arkady Berenstein
University of Oregon Abstract In my lecture I will discuss a class of rational recursions that, rather surprisingly, turn out to be integer sequences. For example, the rational recursion x_{k+1}=(x_k^2+1)/x_{k-1} with x_1=x_2=1 for n=3,4,5,6,... gives is 2,5,13,34,..., (this is a half of the Fibonacci sequence). In fact, the ultimate reason for integrality is that each x_n is a Laurent plynomial over integers in x_1 and x_2. For instance, x_5=x_1/x_2^2 + 2/x_1 + 2/(x_1^2x_2^2) + x_2^4/x_1^3 + 3 x[2]^2/x_1^3 + 3 x_2^4/x_1^3 + 1/(x_1^3x_2^2) which gives x_5=13 when x_1=x_2=1. This is an example of what cluster recursions are: they are rational recursions of order n with the property that each member of the sequence is a Laurent polynomial in x_1,...x_n. In my lecture I will give more examples of "one-dimensional" cluster recursions such as x_{k+1}=(x_k^b+1)/x_{k-1}, where b is a positive integer, x_{k+1}x_{k-3}=x_k x_{k-2}+x_{k-1}^2 (Somos-4) some "two-dimensional" ones like: x_{i,j+1}x_{i,j-1} = x_{i+1,j}x_{i-1,j} + x_{ij}^2 (Q-system of type A) and many others. The explanation of the integrality of these sequences and the underlying Laurent Phenomenon is in the realm of cluster algebras that were introduced by A. Zelevinsky and S. Fomin in 2001. I will conclude the lecture with appropriate definitions of cluster mutations and algebras and will demonstrate how the above examples fit to the general cluster framework. | |
| Time and Place: | 4:30 PM CW 146 |
| TUESDAY Mar. 27 : | Operator Algebras Seminar |
| Title: | Set theory background: independence proofs and forcing |
| Sarah Reznikoff
Kansas State University We continue proving the Fundamental Theorem of Forcing | |
| Time and Place: | 1:00 PM 204 Burt Hall |
| FORTY-SEVENTH WILLIAM J. SPENCER LECTURE | |
| Title: | Quantum Cluster Algebras |
| Arkady Berenstein
University of Oregon Abstract: Cluster algebras have been introduced by Fomin and Zelevinsky in 2001 as an algebraic framework for total positivity and canonical bases in representations of reductive groups. Now the theory of cluster algebras is connected to many different areas of mathematics, for example, representation theory of finite dimensional algebras, Poisson geometry and Teichmuller Theory. The goal of my talk (based on joint work with A. Zelevinsky) is to introduce quantum deformations of cluster algebras. While a cluster algebra corresponds to an integer skew-symmetrizable matrix B, its quantum version corresponds to a compatible pair of B with a skew-symmetric matrix responsible for the q-commutation relations. It turns out that all "classical" cluster structures can be carried over (sometimes conjecturally) to the quantum world. For instance, we expect that each quantum reductive group admits a quantum cluster structure. Same is expected for each double Bruhat cell in quantum Kac-Moody groups. Ultimately, I will explain how to fulfill one of the original goals of the cluster project: construction of the "canonical" basis in acyclic case. | |
| Time and Place: | 2:30 PM CW 102 |
| M-Seminar | |
| Title: | Fourier transforms in the SYZ programme |
| Chit Ma,
Chinese University of Hong Kong Abstract: The Strominger-Yau-Zaslow programme says that there should be a theory of fiberwise Fourier transforms along special Lagrangian fibrations which would explain mirror symmetry. This programme has been verified successfully in special cases when quantum corrections do not arise. We will describe a theory of Fourier transforms of flat branes on tori and how it can be applied in the family setting. And in certain special circumstances this explains quantum corrections in SYZ transformations. | |
| Time and Place: | 3:30 PM CW 120 |
| Number Theory Seminar | |
| Title: | Lind-Lehmer constants for Z_p*Z_p |
| Dilum De Silva
Kansas State University We will talk about the Lind-Lehmer constant for the group Z_3*Z_3 and see how we can generalize the idea for Z_p*Z_p. | |
| Time and Place: | 3:30 PM Cardwell 122 |
| WEDNESDAY Mar. 28 : | Algebra Seminar |
| Title: | Quantum Hankel algebras |
| Arkady Berenstein
University of Oregon Abstract In my talk (based on joint work with David Kazhdan) I will introduce a class of quantum Hankel algebras which are: (1) flat deformations of polynomial algebras, (2) admit a number of automorphisms and same number of derivations. The simplest example is the quadratic algebra H_1 generated by {X_n}, where n runs over integers, with a single relation X_1X_0=qX_0X_1, where q is not a root of unity and the remaining relations coming from an automorphism and a derivation of H_1 both sending X_n to X_{n+1}. Quite surprisingly, H_1 is a flat deformation of polynomials in infinitely many variables and: (a) admits a canonical basis, (b) has quantum cluster structure, (c) contains a q-deformation of the so called Q-system of type A (the latter one is the set of characters of Kirillov-Reshetikhin modules over affine quantum groups of type A), (d) each member of this q-deformed Q-system is a quantum Hankel determinant in {X_n}, (e) each subalgebra of H_1 generated by X_1,...,X_n is a flat deformation of polynomials in n variables. I will also define the "k-dimensional" quantum Hankel algebra H_k whose generators are labeled by the k-dimesnional lattice Z^k and whose relations are determined by some basic ones and by k automorphisms and k derivations; and will demonstrate that these algebras share many properties of H_1. If time permits, I will explain that the flatness of H_k and its generalizations follows from the (no less surprising) observation that Hecke algebras "look like" Hopf algebras, which allows to produce many new solutions of the quantum Yang-Baxter equation (QYBE) out of a given initial one. | |
| Time and Place: | 3:30 PM TBA |
| Analysis Seminar | |
| Title: | Conjectures about harmonic measure |
| Istvan Prause
University of Helsinki Abstract: How harmonic measure is distributed on the boundary of a simply connected domain? This is a long-standing open problem. I will discuss a two-sided perspective and present some partial results in the quasiconformal category. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Mar. 29 : | FORTY-EIGHTH WILLIAM J. SPENCER LECTURE |
| Title: | Conformal Welding |
| Donald Marshall
University of Washington Abstract: Conformal mapping has been a useful tool in science and engineering. Most classical uses involve transplanting a differential equation (such as Laplace's equation) on a complicated region to a simpler region, then pushing the solution on the simpler region back to the original region. Since few conformal maps can be given by an explicit formula, other numerical techniques must be used. In this talk we'll give an elementary method that is fast and accurate. We'll focus on modern applications to conformal welding including recent developments in vision recognition ("the fingerprint" of a region), spectra of certain ODEs, Cauchy transforms of positive measures, trees (graphs), and lemniscates. | |
| Time and Place: | 2:30 PM TH 1018 |
| Function Theory Study Seminar | |
| Title: | A survey of discrepancy theory |
| Dmitriy Bilyk,
University of South Carolina Abstract: Geometric discrepancy theory seeks answers to various versions of the following questions. How well can one approximate a continuous distribution by a discrete one? And what are the limitations and errors that necessarily arise? I will talk about the main results, constructions, and ideas of the theory, which stem in particular from number theory and harmonic analysis -- the two fields that have played a pivotal role in the development of the field. | |
| Time and Place: | 3:30 PM CW 143 |
| THIRD M-CENTER LECTURE | |
| Title: | Constructible Sheaves and Mirror Symmetry |
| Eric Zaslow
Northwestern University I will review some results relating the theory of constructible sheaves to the Fukaya category, and the relation to mirror symmetry for toric varieties. With this in hand, I will then discuss conjectural constructible models of the categories involved in mirror symmetry of Calabi-Yau manifolds at the large complex / large radius limit points. | |
| Time and Place: | 3:30 PM CW 146 |
| Mathematics Education Seminar | |
| Title: | Mathematical Tasks and Student Cognition |
| Sherri Martinie
Kansas State University College of Education We will focus discuss Henningsen and Stein's article, "Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning". This paper focuses on examining and illustrating how classroom-based factors can shape students' engagement with mathematical tasks that were set up to encourage high-level mathematical thinking and reasoning. Little research has been done on the kinds of instructional environments required to support the implementation of tasks. This paper addresses that gap. It uncovers both challenges of implementing high-level tasks and support for high-level tasks | |
| Time and Place: | 4:30 PM CW 122 |
| MONDAY Apr. 02 : | Topology seminar |
| Title: | An introduction to the Higher Seifert van Kampen theorem |
| Dany Majard
Kansas State University Abstract: In two weeks R.Brown will be visiting our Department. This talk is an invitation to get accustomed to his work. After a quick reminder of the original SvKT, I will explain the limitations of groups and show how higher dimensional category theory was the key to opening the true potential of Homotopy. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | TBA |
| Georgia Benkart
University of Wisconsin, Madison Abstract TBA | |
| Time and Place: | 4:30 PM CW 146 |
| TUESDAY Apr. 03 : | Operator Algebras Seminar |
| Title: | Set theory background: independence proofs and forcing |
| Sarah Reznikoff
Kansas State University We go over (most of) the forcing proof that the combinatorial principle Diamond is consistent with ZFC. | |
| Time and Place: | 1:00 PM 204 Burt Hall |
| Faculty Meeting | |
| Title: | Faculty Meeting |
| . | |
| Time and Place: | 2:30 PM CW 122 |
| M-Seminar | |
| Title: | On the eigenvalue spectrum of the Inertia operator |
| Kai Behrend,
University of British Columbia Abstract: We study the question whether the inertia operator on the Grothendieck module of algebraic stacks is diagonalizable. Answering this question may shed light on some of the mysterious operations defined by Joyce in his work on stack functions. This is joint work with Pooya Ronagh. | |
| Time and Place: | 3:30 PM CW 120 |
| Function Theory Study Seminar | |
| Title: | Thermodynamics, dimension and the Weil-Petersson metric |
| Oleg Ivrii
Harvard University We will explain some ideas from the paper of Curt McMullen "Thermodynamics, dimension and the Weil-Petersson metric". | |
| Time and Place: | 3:30 PM CW 101 |
| WEDNESDAY Apr. 04 : | Analysis Seminar |
| Title: | Ghosts of the Mapping Class Group |
| Oleg Ivrii
Harvard University Abstract:Recently, McMullen showed that the Weil-Petersson metric in Teichmuller theory arises as the double derivative of the Hausdorff dimension of certain families of quasi-circles arising from simultaneous uniformization. He noticed that a similar construction can be carried out on spaces of Blaschke products; and so by analogy one can define a Weil-Petersson metric there. But how does this metric look like? Is it incomplete? Invariant under the mapping class group? While it appears that there is no genuine mapping class group acting on the space of Blaschke products, there are ‘ghosts' acting on two very different boundaries that arise from non-tangential and horocyclic degenerations. In this talk, we will describe these boundaries and illuminate these ghosts. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Apr. 05 : | Mathematics Education Seminar |
| Title: | Effective Visual Tools for Teaching Mathematics |
| Andrew Bennett
Kansas State University This will be a sort of rambling overview of what is and is not known about developing effective visual tools for teaching mathematics. We will start with the history of the use of "visualizations" in mathematics education and then look at some recent survey articles that discuss what we know and what questions need to be answered. This can lead to a discussion of how best to design "touchable math" tools. | |
| Time and Place: | 4:30 PM CW 122 |
| MONDAY Apr. 09 : | Topology seminar |
| Title: | A classification of Taylor towers from spaces to spectra |
| Michael Ching
Amherst College Abstract: This talk is about the Goodwillie calculus of functors from the category of based spaces to the category of spectra. The goal is to describe additional structure possessed by the derivatives of these functors that captures the extensions in the Taylor tower and thus allows the tower to be reconstructed. I'll give a review of Goodwillie's homotopy calculus in this context, and then describe how the additional structure on the derivatives arises from properties of the cross-effects of these functors. We will see that partially-stabilized cross-effects form right modules over the (Koszul duals of the) E_n-operads, and observe that the limiting structure on the derivatives is that of a divided power right module over the derivatives of the identity. | |
| Time and Place: | 3:30 PM CW 120 |
| TUESDAY Apr. 10 : | Operator Algebras Seminar |
| Title: | More set theory and functional analysis |
| Ilijas Farah
York University Farah's second talk of the day, to be delivered first, will be a little more specialized to an audience moderately knowledgeable about operator algebras. | |
| Time and Place: | 1:00 PM 204 Burt Hall |
| COLLOQUIUM | |
| Title: | Necessary Applications Of Set Theory In Functional Analysis |
| Ilijas Farah
York University, Ontario Abstract: Operator algebras and abstract set theory were once considered to be only superficially related, but exciting connections and deep theorems have been discovered during the last few years. I will discuss applications of set theory to operator algebras, both necessary and 'unnecessary' ones. | |
| Time and Place: | 2:30 PM CW 122 |
| This lecture is supported in part by the Advanced Distinguished Lecture series. | |
| M-Seminar | |
| Title: | Algebraic structures in perturbative quantum field theory |
| Kevin Costello,
Northwestern University Abstract: I'll discuss my work with Owen Gwilliam, where we develop an approach to perturbative quantum field theory which is similar to the deformation-quantization approach to quantum mechanics. From this point of view, the theory of renormalization provides a proof that we can deform a classical algebraic structure into a quantum one. | |
| Time and Place: | 3:30 PM CW 120 |
| THURSDAY Apr. 12 : | EIGHTH BRENT P. SMITH MEMORIAL LECTURE |
| Title: | The Prescient Ramanujan |
| George Andrews
Pennsylvania State University Abstract: The discovery of Ramanujan's Lost Notebook in 1976 provided a number of surprises. Often Ramanujan had anticipated in 1919-1920 (and, in fact, gone beyond) many results found by others in the last half of the 20th century. I shall discuss a number of these related to continued fractions, partitions, and other number-theoretic topics. I will conclude with a partition function difference problem solved partially by Richmond and Szekeres in 1978. This problem was effectively fully solved in the Lost Notebook, and its study has led to some unexpected consequences. | |
| Time and Place: | 2:30 PM TH 1018 |
| Mathematics Education Seminar | |
| Title: | Continuous Quantitative Reasoning |
| Carlos Castillo-Garsow
Kansas State University This talk addresses four primary questions: "What is continuous reasoning?" "Why is continuous reasoning important?" "How does someone reason both continuously and quantitatively?" and "How can we aid students in building continuous quantitative reasoning?" Experimental results (Bassock & Olseth, 1995; Castillo-Garsow, 2010) are used to highlight key distinctions in determining the meaning and role of continuous reasoning. These results are then placed in the context of a theoretical framework (P. W. Thompson, 2011, 2008a, 1990) that develops the meaning of continuous quantitative reasoning. | |
| Time and Place: | 4:30 PM CW 122 |
| SATURDAY Apr. 14 : | Keynote Address - 2012 MAA Kansas Section Meeting |
| Title: | The Story of Ramanujan's Lost Notebook |
| George Andrews
Pennsylvania State University In 1976, owing to a variety of serendipitous accidents, I visited the Wren Library at Trinity College of the Univeristy of Cambridge and happened upon a collection of letters and manuscripts written by Ramanujan including a 100+ page document. These papers had been sitting in a box that was given to the Wren Libray in the mid-1960's and had not been opened previously. I titled this collection "Ramanujan's Lost Notebook" to distinguish it from the famous notebooks that he had prepared earlier in his life. On and off for the past 35 years, I have studied these wild and confusing pages. Bruce Berndt and I are preparing a five volume account of the Lost Notebook. Some of the weirder results have yielded entirely new lines of research. I will try to provide a gentle account of where these efforts have led. I will conclude with a couple of stories about associated TV and film projects that arose because of this discovery. | |
| Time and Place: | 11:00 AM CW 102 |
| MONDAY Apr. 16 : | Topology seminar |
| Title: | A nonabelian tensor product of groups and homotopical applications |
| Ronnie Brown
Bangor University Abstract: This nonabelian tensor product is available for groups which act on each other, and on themselves by conjugation. It allows for a factorization of the commutator map $G \times G \to G$ through a morphism $\kappa: G \otimes G \to G$, whose kernel is of homotopical interest, since it is isomorphic to $\pi_3 SK(G,1)$. This allows for specific computations, especially as $G \otimes G$ is finite if $G$ is finite. The route to this isomorphism is through a van Kampen type theorem for $n$-cubes of spaces, which itself is part of the philosophy of not looking at plain topological spaces but at spaces with structure which reflects the way they are constructed. | |
| Time and Place: | 3:30 PM CW 120 |
| For more information see www.bangor.ac.uk/r.brown/nonabtens.html | |
| Algebra Seminar | |
| Title: | On higher algebraic K-theory |
| Alexander Rosenberg
Kansas State University Abstract TBA | |
| Time and Place: | 4:30 PM CW 146 |
| TUESDAY Apr. 17 : | FORTY-NINTH WILLIAM J. SPENCER LECTURE |
| Title: | Motion, Space, Knots, and Higher-dimensional Algebra |
| Ronald Brown
School of Computer Science Bangor University Abstract: The notion of mathematical space is important for encoding data for motion. To understand the structure of various kinds of space we need forms of representation, and in the end some kind of algebra to perform computations. We illustrate these ideas with the Dirac String Trick and a video explaining it, and then move on to use algebra to study the space around a knot. A new method in mathematics is “higher dimensional algebra”, in which we can have formulae and their manipulation in dimension 2, or higher, rather than the usual restriction essentially to a line, which is desirable for computation, but not necessarily for description. Mathematics has also come up with new conceptual ways of describing way some complicated structures are put together from simple ones, using analogies from across widely different parts of mathematics. This way of using abstraction for analogy and comparison is one of the powers of mathematics. | |
| Time and Place: | 2:30 PM CW 102 |
| M-Seminar | |
| Title: | Stable complexes and Fourier-Mukai transforms |
| Jason Lo,
University of Missouri Abstract: Fourier-Mukai transforms have been used to understand the relationships between various moduli spaces of sheaves, such as in the work of Bruzzo-Maciocia and Bridgeland-Maciocia. In this talk, I will give two examples - one on K3 surfaces and one on elliptic threefolds - where a moduli of complexes is mapped into a moduli of sheaves via a Fourier-Mukai transform. | |
| Time and Place: | 3:30 PM CW 120 |
| WEDNESDAY Apr. 18 : | Analysis Seminar |
| Title: | tba |
| Todd Easton
Kansas State University Abstract | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Apr. 19 : | THIRTIETH ANNUAL FRIENDS OF MATHEMATICS LECTURE |
| Title: | What Do Fermat's Last Theorem and Electro-magnetic Duality Have In Common? |
| Edward Frenkel
University of California, Berkeley Abstract: Fermat's Last Theorem may be viewed as a spectacular application of the Langlands Program, bringing together Number Theory and Harmonic Analysis. These ideas have propagated to other areas of mathematics, such as algebraic geometry and representation theory of infinite-dimensional Lie groups and Lie algebras. And in recent works by Witten and others, it was shown that the Langlands duality patterns are closely related to the electro-magnetic duality of four-dimensional quantum gauge theory. I will give an overview of these connections. | |
| Time and Place: | 2:30 PM TH 1018 |
| Topology seminar | |
| Title: | TBA |
| Ronnie Brown
Bangor University Abstract: TBA | |
| Time and Place: | 3:30 PM CW 146 |
| Mathematics Education Seminar | |
| Title: | Characterizing Student' Use of Integrals in Physics with Resource Graphs |
| Dehui Hu
KSU Physics Education Research Group Developing the skills to set up integrals is critical for students' success in calculus-based physics. It requires a high level of understanding of both math and physics concepts. The goal of this study is to investigate how students organize their knowledge in math and physics when setting up integrals in electricity & magnetism topics. In our study, 13 engineering physics II students are organized in group problem solving sessions using white boards. We use resource framework to identify the various ideas associated with math and physics concepts students bring in. Then we use the representation of resource graph (Michael C. Wittmann, 2006) to characterize how students coordinate different resources in a specific physics context. In this talk, we will present the resource graphs for one group of student. This can lead to a discussion of why students have difficulties with using integrals in physics. | |
| Time and Place: | 4:30 PM CW 122 |
| THIRTIETH ANNUAL FRIENDS OF MATHEMATICS AWARDS BANQUET | |
| Title: | Mathematics with a Human Face |
| Edward Frenkel
University of California, Berkeley Abstract: There is a strange paradox: On the one hand, an increasingly larger part of our life is based on mathematics. On the other hand, this very important part of our existence remains hidden from most people and has become almost a taboo. I will talk about how this happened and what we can do to change it. | |
| Time and Place: | 6:00 PM K-State Student Union |
| 2nd Floor Concourse and Main Ballroom | |
| DISTINGUISHED ALUMNUS CLASS OF 1961 | |
| Title: | Wow! My Math Instructors Sent Me On Some Journey! |
| Chet Wilcox
Naval Meteorology and Oceanography Command Stennis Space Center, MS, retired Abstract: My undergraduate math instructors sent me off on a long journey. They gave me the itinerary for my career, but it contained only the first stop. Once there, they said to use my math degree as a start, work hard, and the rest of the itinerary will materialize. Forty wonderful years and many delightful stops later, I hitched my final ride -- into retirement! Those instructors sent many others off on similar journeys, and most of us never returned to thank them. But we can thank their successors now engaged in the same important work of teaching undergraduate math. Thank you for the great job! Trust me, fifty years from now your students will all be wishing they could find you and say, “Thanks for the ride!” | |
| Time and Place: | 6:00 PM K-State Student Union |
| 2nd Floor Concourse and Main Ballroom | |
| MONDAY Apr. 23 : | Topology seminar |
| Title: | Context-free manifold calculus and the operad of framed discs |
| Victor Turchin
Kansas State University Abstract: The goal of the talk is to show how the operad of framed discs appears in the manifold calculus of functors. Namely if a functor is context-free then its Weiss polynomial approximations can be expressed as spaces of derived maps between truncated right modules over this operad. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | On higher algebraic K-theory II |
| Alexander Rosenberg
Kansas State University | |
| Time and Place: | 4:30 PM CW 146 |
| TUESDAY Apr. 24 : | Faculty Meeting |
| Title: | Faculty Meeting |
| . | |
| Time and Place: | 2:30 PM CW 122 |
| WEDNESDAY Apr. 25 : | Analysis Seminar |
| Title: | tba |
| tba | |
| Time and Place: | 4:30 PM Cardwell 122 |
| Analysis Seminar | |
| Title: | Bilinear Square Functions and Vector-Valued Calderón-Zygmund Operators |
| Jarod Hart,
University of Kansas Square functions have become a useful tool in harmonic analysis through their close connection with Littlewood-Paley-Stein estimates. There have been a number of results involving bounds of different types of square functions in a bilinear setting. The focus of this talk is to prove product Lebesgue space bounds for square functions associated to bilinear operators satisfying Calderón-Zygmund type kernel conditions. I will present boundedness results on the full range of Lebesgue space exponents that can be expected, including some non-Banach space bounds. Almost orthogonality estimates, the Fefferman-Stein maximal function inequality, and linear Littlewood-Paley-Stein Theory are employed to prove bounds in the Banach space setting. To extend bounds to the full range of Lebesgue space exponents, vector-valued bilinear Calderón-Zygmund operators are introduced. These square function bounds are used to provide a new proof of the bilinear T(1) Theorem and prove a bilinear T(b) Theorem. | |
| Time and Place: | 4:30 PM Cardwell 122 |
| THURSDAY Apr. 26 : | Function Theory Study Seminar |
| Title: | Some dimension reduction methods in multivariate regression |
| Kun Chen
Kansas State University Abstract: We develop some new methods for fitting multivariate regression model by seeking certain low dimensional structures of the coefficient matrix related to its singular value decomposition (SVD). A weighted nuclear-norm penalized method is proposed for simultaneous rank reduction and coefficient estimation. The rank estimation consistency and the prediction performance bound are established. We then propose a reduced-rank regression with sparse SVD approach, in which we prompt the sparsity in both the singular values and the singular vectors of the coefficient matrix for conducting simultaneous multi-level variable selection and rank reduction. We show that both the rank and the sparse SVD structure can be correctly identified with probability approaching one as the sample size increases. Several applications from the areas of genetics and ecology showcase the effectiveness of the proposed methods. | |
| Time and Place: | 3:30 PM CW 143 |
| Mathematics Education Seminar | |
| Title: | A review of the arguments for and against minimally guided instruction |
| Paul Irving
Kansas State University Physics Education Research Group Kirschner, Sweller and Clark started with the publication of their paper in 2006, a debate that still continues today, about the validity of using minimal guidance instruction. Much of the basis of their arguments on the inappropriateness of minimal guidance instruction is based on the theory of human cognitive architecture and specifically the effects minimal guidance has on cognitive load. This talk discusses the claims made in the 2006 paper and subsequent publications on the matter making reference to both the arguments and defences presented so far in literature. The talk specifically questions the validity of the arguments for and against the use of problem-based learning as it is a minimally guided learning environment in which I have a great deal of experience. I will argue that many of the debates about the effectiveness of problem-based learning arise from misconceptions of what constitutes problem-based learning and the multiple interpretations of self-directed and student-centered learning. It is also argued that the outcomes from the evaluation of any problem-based learning course (or minimally guided designed course) can only be interpreted and discussed in the context of that particular model and the environment within which it was implemented. | |
| Time and Place: | 4:30 PM CW 122 |
| MONDAY Apr. 30 : | Topology seminar |
| Title: | From beads to quilts: what 2-Morse functions tell us about 2-Manifolds. |
| Dany Majard
Kansas State University Abstract: Beyond this humorous title lies an important truth: Morse functions are fantastic to analyse 1 and 2 manifolds but their power diminishes exponentially as dimensions grow. I will show how it is so and what one can do to go around it. Basic knowledge of category theory and differential geometry are a plus. This talk should be rich in pictures. | |
| Time and Place: | 3:30 PM CW 120 |
| Algebra Seminar | |
| Title: | Kac Conjecture and counting representations |
| Zongzhu Lin
Kansas State University Abstract: Given an arbitrary finite quiver, one associates a symmetric generalized Cartan matrix, which defines a Kac-Moody Lie algebra which has a root system and root space decomposition. In late 70's Kac studied the relations of positive roots and indecomposable representations of the quiver and proved that there is an indecomposable representation of a given dimension vector if and only of the dimension vector is a positive root of the corresponding Lie algebra. One considers the representations of the quiver over finite field with q elements and counts the number of absolutely indecomposable representations of a fixed dimension vector. In 1982, Kac conjectures that this number is a polynomial of q as one varies the finite fields, the coefficients are non-negative integers, and the constant term is exactly the dimension of the root space of the Kac-Moody Lie algebra of the root being exactly the dimension vector. ═In this seminar talk, I will outline the proof posted by Hausel et al a few days ago. The proof of the both parts of the conjecture relies on Jiuzhao Hua's thesis work on counting the number of representations. Hua was a postdoc here at K-State during 1998-1999. I will also discuss new questions in further understanding of the Kac conjecture. | |
| Time and Place: | 4:30 PM CW 146 |
| THURSDAY May. 03 : | NINTH BRENT P. SMITH MEMORIAL LECTURE |
| Title: | Reduced Models You Can Believe In |
| Jan Hesthaven
Brown University Abstract: In this talk we present an overview of recent and ongoing efforts to develop reduced basis methods for which one can develop a rigorous a posteriori theory, hence certifying the accuracy of the reduced model for parametrized linear PDEs. This is in contrast to most previous attempts to develop reduced complexity methods that, while used widely and of undisputed value, are often heuristic in nature and the validity and accuracy of the output is often unknown. This limits the predictive value of such models. We outline the theoretical and computational developments of certified reduced basis methods, drawing from problems in electromagnetics and acoustics. The performance of the certified reduced basis model will be illustrated through a number of examples to highlight the major advantages of the proposed approach and discuss challenges associated with high-dimensional problems. | |
| Time and Place: | 2:30 PM TH 1018 |
| Function Theory Study Seminar | |
| Title: | On geometric rigidity and analysis on metric spaces after some notes of M. Bonk. |
| Pietro Poggi-Corradini
Kansas State University Abstract In this talk a sketch of the proof of the celebrated Mostow Rigidity Theorem will be given. A particular attention will be paid to the analytic part of the proof. | |
| Time and Place: | 3:30 PM CW 143 |
| Mathematics Education Seminar | |
| Title: | Assessment of student presentations about integration in a physics context |
| Josh Von Korff
Kansas State University Physics Education Research Group Assessing student understanding of integration can be challenging, because quantitative metrics have limited validity. I will present several examples of student work on integration problems in introductory mechanics, along with proposed assessment mechanisms. I will invite the audience to provide input regarding the face validity of these mechanisms. | |
| Time and Place: | 4:30 PM CW 122 |
| THURSDAY May. 10 : | Function Theory Study Seminar |
| Title: | Rectifiable curves in metric spaces |
| Hrant Hakobyan
Kansas State University Abstract When a metric space contains many rectifiable curves it often has nice properties such as linear local connectivity, quasiconvexity, Poincare inequalities etc. I will discuss some of these definitions and give several examples. In particular I will talk about these two examples: 1) there is a totally disconnected set E of Hausdorff dimension 1 in the plane such that C\E in not quasiconvex, 2) Sierpinski carpet does not satisfy Poincare Inequality. Connections to conformal dimension will also be discussed. | |
| Time and Place: | 3:30 PM CW 143 |
| THURSDAY May. 17 : | Function Theory Study Seminar |
| Title: | Rectifiable curves in metric spaces II |
| Hrant Hakobyan
Kansas State University Abstract: When a metric space contains many rectifiable curves it often has nice properties such as linear local connectivity, quasiconvexity, Poincare inequalities etc. I will discuss some of these definitions and give several examples. In particular I will talk about these two examples: 1) there is a totally disconnected set E of Hausdorff dimension 1 in the plane such that C\E in not quasiconvex, 2) Sierpinski carpet does not satisfy Poincare Inequality. Connections to conformal dimension will also be discussed. | |
| Time and Place: | 3:30 PM CW 143 |