Algebra Seminar, Mathematics, Kansas State University, Fall 2007

Algebra Seminar
Department of Mathematics
Kansas State University
Fall 2007
Monday, 4:30pm-5:20pm
Cardwell Hall 131
Click here to learn more about the algebra research group at Kansas State University

Speaker: Gerald Hoehn, Kansas State University
Title: Conformal designs based on Vertex Operator algebras I
Abstract: In this talk I will give a brief introduction what is a design, in particular what is a spherical design. Designs related to projective spaces of grassmanians over finite fields and lattices.

Speaker: Gerald Hoehn, Kansas State University
Title: Conformal designs based on Vertex Operator algebras II
Abstract: In this talk I will introduce the concept of conformal design and its relations with vertex operator algebras.

Speaker: Aderemi Kuku, University of Iowa and ICTP, ITALY
Title: Introduction to Algebraic Theory and Some Applications
Abstract: MThe lecture will contiue on Sept 26, 27, 28 all in TH 1021

October 1: Special lecture by Professor Kuku in CW 129 2:30pm-4:30pm (No class today)

Speaker: Aderemi Kuku, University of Iowa and ICTP, ITALY
Title: Introduction to Algebraic Theory and Some Applications
Abstract: The lecture will continue on Oct. 2 (CW 129), Oct 3 (TH 1021) all at 4:30pm-5:20pm

Speaker: cancelled (moved to the last week for eight talks by Professor Kuku)
Title: p
Abstract: M

Speaker: Li Guo, Rutgers University
Title: Rota-Baxter algebra, operads and Hopf algebras
Abstract: A Rota-Baxter algebra is an algebra R
with a linear map P: R-> R such that for any x, y in R,
P(x)P(y)=P(xP(y))+P(P(x)y)+\lambda P(xy)
where lambda is a constant. We consider a class of regular,
binary, quadratic operads related to Rota-Baxter algebra
and their Hopf algebras.

Speaker: Zongzhu Lin, Kansas State University
Title: Tilting Theory and Derived Categories
Abstract: Morita equivalence is a way to establish equivalences between the module categories of two algebras. The tilting theory is way to provide equivalences between derived categories. This theory has been used recently to establish equivalences between two triangular categories as well as cluster algebras. This is only a survey type talks on the theory and is aimed to provide some background on the topic for further applications.

Speaker: Zongzhu Lin, Kansas State University
Title: Titling complexes and derived Morita equivalence
Abstract: Happel use tilting modules to establish derived equivalence between two algebras. In this talk, I will summarize Rickard's result of derived Morita equivalence using tilting complexes.

Speaker: Jennifer Paulhus, Kansas State University
Title: Decomposing Jacobian varieties of curves with extra automorphisms.
Abstract: Given a curve X with non-trivial automorphism group G, we
discuss ways to decompose the Jacobian variety of X. In particular, we
are looking for Jacobian varieties that have many copies of an elliptic
curve as factors. The techniques employed involve idempotent relations
in the group ring Q[G] as well as special characters of the group G.

Speaker: Jennifer Paulhus, Kansas State University
Title: Decomposing Jacobian varieties of curves with extra automorphisms. II
Abstract: Given a curve X with non-trivial automorphism group G, we
discuss ways to decompose the Jacobian variety of X. In particular, we
are looking for Jacobian varieties that have many copies of an elliptic
curve as factors. The techniques employed involve idempotent relations
in the group ring Q[G] as well as special characters of the group G.

Speaker: Yiqiang Li, Yale University
Title: Geometric realization of canonical basis for irreducible representations of quantum groups
Abstract:. Let U be a quantum group. In this talk, I will discuss a geometric realization of certain simple U-modules and their canonical bases, via certain simple perverse sheaves on open subvarieties of the representation spaces of a quiver.

Speaker: Jennifer Paulhus Kansas State University
Title: Decomposing Jacobian varieties of curves with extra automorphisms. III
Abstract: Given a curve X with non-trivial automorphism group G, we discuss ways to decompose the Jacobian variety of X. In particular, we are looking for Jacobian varieties that have many copies of an elliptic curve as factors. The techniques employed involve idempotent relations in the group ring Q[G] as well as special characters of the group G

Speaker: Ralf Schiffler,University of Massachusetts at Amherst
Title: Quiver Representations: Basic Facts and Some Recent Developments.
Abstract: This talk is an introduction to quiver representations. A quiver (or oriented graph) Q=(Q_0,Q_1) is a set of vertices Q_0 and set of arrows Q_1 such that each arrow a in Q_1 starts at some vertex s(a) in Q_0 and ends at some vertex t(a) in Q_0. A representation of the quiver Q consists of a vector space V_i for each vertex i in Q_0 and a linear map f_a from V_{s(a)} to V_{t(a)} for each arrow a in Q_1. We will introduce the category of representations of such a quiver Q, consider an equivalent realization as module category over the path algebra of Q and explain basic Auslander-Reiten theory. We will also illustrate some recent developments that connect quiver representations to cluster algebras.