Spring 2020
Date 
Period

Time

Location

Speaker

Topic


January 17  9  4:05 – 4:55  LIT 368  Tom Wolf  An overview of character theory 
January 24  9  4:05 – 4:55  LIT 368  Tom Wolf  Non vanishing elements of finite solvable groups 
February 4  4  10:40 – 11:30  LIT 368  Eric Moorhouse  Ovoids from lattices (Join Seminar with Combinatorics) Abstract 
February 14  9  4:05 – 4:55  LIT 368  Richard Crew  Valuations in Algebraic Geometry
Abstract: Valuations of height greater than one were first used by Zariski in his work on the desingularization of algebraic surfaces in 3folds, and have on occasion been used in other investigations where the language of schemes is not so helpful. Huber’s theory of adic spaces uses valuation theory in a nontrivial way, and Peter Scholze’s theory of perfectoid spaces is built on Huber’s theory. In these talks I will explain the basic ideas and give some simple (and notsosimple) examples. The setting will be algebraic throughout, but with some asides to the theory of nonarchimedean spaces. In this first talk I will review some basic facts about valuations and valuation rings, define the valuation spectrum of a ring, and if time permits prove Zariski’s theorem that the valuation spectrum of a field is quasicompact. 
February 21  9  4:05 – 4:55  LIT 368  Richard Crew  Valuations in Algebraic Geometry, continued
Abstract: Valuations of height greater than one were first used by Zariski in his work on the desingularization of algebraic surfaces in 3folds, and have on occasion been used in other investigations where the language of schemes is not so helpful. Huber’s theory of adic spaces uses valuation theory in a nontrivial way, and Peter Scholze’s theory of perfectoid spaces is built on Huber’s theory. In these talks I will explain the basic ideas and give some simple (and notsosimple) examples. The setting will be algebraic throughout, but with some asides to the theory of nonarchimedean spaces. In this first talk I will review some basic facts about valuations and valuation rings, define the valuation spectrum of a ring, and if time permits prove Zariski’s theorem that the valuation spectrum of a field is quasicompact. 
February 28  9  3:00 – 3:50  LIT 368  Peter Sin  Title: ErdősKoRado properties of permutation groups.
Abstract: The ErdősKoRado (EKR) theorem is a famous result in extremal combinatorics answering the question: In a set of size n, how many subsets of size k can there be such that any two have nonempty intersection, and what are the maximum family of subsets? We can assume n≤2k. The EKR Theorem states that there are at most binom(n1,k1) subsets in such a family, and for n>2k any family attaining the maximum is obtained by taking all subsets of size k having a common element. This result turns out to have many analogies when sets are replaced by other combinatorial objects. There is a whole book on this theme by Godsil and Meagher. I will discuss EKR problems in permutation groups and if time allows, I will present recent joint work with Karen Meagher which proves 
March 6  9  4:05 – 4:55  LIT 368  No seminar  Spring break 
March 13  9  4:05 – 4:55  VIA ZOOM  Peter Sin  Title: ErdősKoRado properties of permutation groups (continued).
Abstract: The ErdősKoRado (EKR) theorem is a famous result in extremal combinatorics answering the question: In a set of size n, how many subsets of size k can there be such that any two have nonempty intersection, and what are the maximum family of subsets? We can assume n≤2k. The EKR Theorem states that there are at most binom(n1,k1) subsets in such a family, and for n>2k any family attaining the maximum is obtained by taking all subsets of size k having a common element. This result turns out to have many analogies when sets are replaced by other combinatorial objects. There is a whole book on this theme by Godsil and Meagher. I will discuss EKR problems in permutation groups and if time allows, I will present recent joint work with Karen Meagher which proves 
March 20  9  4:05 – 4:55  LIT 368  No Seminar  This week 
March 27  9  4:05 – 4:55  LIT 368  No Seminar  This week 
April 3  9  4:05 – 4:55  LIT 368  No Seminar  This week 
April 10  9  4:05 – 4:55  LIT 368  No Seminar  This week 
April 17  9  4:05 – 4:55  VIA ZOOM  Kevin Keating  The HasseArf Theorem and Nonabelian Extensions 
Fall 2019
Date 
Period

Time

Location

Speaker

Topic


September 20  9  4:05 – 4:55  LIT 305  Peter Sin  Title: The critical group of a graph Abstract: Given a (simple) finite graph, its critical group is a finite abelian group defined by its Laplacian matrix. The group arises in several contexts (Chipfiring games, abelian sandpile model in physics, graph jacobians, arithmetic geometry of curves). I’ll explain the basic definitions and the connection with the MatrixTree Theorem and Chipfiring games. Interesting research topics include trying to compute the critical groups for various families of graphs. This talk is an introduction to this topic, with few prerequisites. 
September 27  9  4:05 – 4:55  LIT 305  Alexandre Turull  pbasic groups Abstract: The rationality of representations of finite groups is best measured as an invariant in the group Q/Z of rational numbers modulo integers under addition. The talk will discuss an effective method to calculate these invariants. The method consists of a series of reductions that eventually reduce the problem to the case when the finite groups are actually $p$basic groups. We will discuss the definition of these $p$basic groups, and the invariants associated with their irreducible characters. 
October 4  9  4:05 – 4:55  LIT 305  No seminar  Homecoming 
October 11  9  4:05 – 4:55  LIT 305  Felix Gotti  Title: The rationalinfinite elasticity property and some related conjectures
Abstract: The elasticity is an algebraic statistic introduced by Valenza in 1990 to measure how much a ring of integers deviates from being a UFD. Since then, the elasticity has been used in more general classes of domains and in commutative monoids. While the elasticity of a domain/monoid belongs to the set $\{x \in \mathbb{R} : x \ge 1\} \cup \{ \infty \}$ by definition, for certain important classes of domains/monoids it turns out to be either rational or infinite, in which case we say that such classes satisfy the rationalinfinite elasticity property. We will see various classes of monoids and integral domains satisfying the rationalinfinite elasticity property as well as classes where such a property is conjectured to hold. 
October 18  9  4:05 – 4:55  LIT 305  Qing Xiang  Fourier analysis on finite abelian groups and uncertainty principles Abstract 
October 25  9  4:05 – 4:55  LIT 305  Zachary Hamaker  Grobner degeneration of matrix Schubert varieties
Abstract: Matrix Schubert varieties are a vast generalization of determinantal varieties, which have been studied since the 19th century in the context of degeneracy loci. I will explain how to use Grobner degeneration, a powerful technique in combinatorial commutative algebra, to compute properties of these varieties. Grobner degenerations are determined by term orders. Historically, people used diagonal term orders, but a major breakthrough by Knutson and Miller showed that antidiagonal terms orders are more natural, and used them to describe the Hilbert series of these varieties combinatorially. Deficiencies of diagonal term orders were discussed in work by Knutson, Miller and Yong. I will outline this history and discuss forthcoming work with Oliver Pechenik and Anna Weigandt where we make new progress with diagonal term orders, including a conjectural way forward in this setting. 
November 1  9  4:05 – 4:55  LIT 305  No seminar  AMS meeting 
November 8  9  4:05 – 4:55  LIT 305  Felix Gotti 
Atomic properties of monoid algebras
Abstract: From any commutative ring $R$ with identity, one can construct the ring of polynomials $R[x]$. If, in addition, $M$ is a commutative monoid, one can construct the monoid algebra $R[x;M]$ over $R$ consisting of all polynomial expressions with coefficients in $R$ and exponents in $M$. It is well known that many algebraic properties such as being an integral domain, being a UFD, and being a Noetherian domain transfer from $R$ to $R[x]$. We will discuss some algebraic and atomic properties that transfer from $R$ (or from $M$) to $R[x;M]$. The question of whether the property of being atomic transfers from $R$ and $M$ to $R[x;M]$ was posed by Robert Gilmer back in the 1980s. It has been recently proved that for any integral domain $R$ the property of being atomic does not transfer from $M$ to $R[x;M]$. We will conclude the presentation talking about such a recent progress.

November 15  9  4:05 – 4:55  LIT 305  Ashleigh Thomas  Modules over polynomial rings with real exponents, as motivated by persistent homology
Abstract: The study of modules over polynomial rings is extended to modules over polynomial rings with real number exponents (these can also be thought of as modules over the group rings k[N^n] and k[R_{\geq0}^n], respectively, where k is a field). We discuss some of the differences between modules in these two settings. For example, Noetherinity does not apply for modules over k[R_{\geq0}^n], but there are alternative finiteness conditions. This exploration is motivated by a data analysis technique called persistent homology, which analyses a system or data set across all values in a parameter space. Persistent homology computations produce modules graded by an input parameter space, which is frequently Z, R, Z^n, or R^n. We give a brief introduction to the basic algebraic constructions used for persistent homology. 
November 22  9  4:05 – 4:55  LIT 305  Kevin Keating  Generic pextensions
Abstract: Let p be prime and let G be a group of order p^n. In this talk I will discuss the existence of polynomials D_i in F_p[X_0,…,X_{i1}] with the following property: For every field K_0 of characteristic p and every Galois extension K_n/K_0 with Gal(L/K)=G there are b_i in K_0 such that K_n is constructed recursively by K_{i+1}=K_i(a_i), with a_i^pa_i=D_i(a_0,..,a_{i1})+b_i. In addition, under mild assumptions on K_0 and b_i, every extension K_n/K_0 constructed this way is Galois with Gal(K_n/K_0)=G. 
November 29  9  4:05 – 4:55  LIT 305  No seminar  Thanksgiving 
Spring 2019
Date 
Period

Time

Location

Speaker

Topic


February 15  9  4:05 – 4:55  LIT 368  Peter Sin  Spreads, Ovoids, Opposites and Irreducible Group Representations
Abstract:
A spread in a polar space is set of disjoint generators (maximal totally isotropic subspaces) that cover the set of points. Dually, an ovoid is set of points such that each generator contains exactly one point from the set. These definitions can be extended to Generalized Polygons, using the concept of oppositeness. I will discuss recent work (with Ihringer and Xiang) on the bounds from representation theory on the size of a partial spreads and partial ovoids. In particular, we show that ovoids cannot exist in the finite Tits octagon.

February 22  9  4:05 – 4:55  LIT 368  Qing Xiang  Characterization of Intersecting Families of Maximum Size in PSL(2, q) (Joint work with Ling Long, Rafael Plaza, and Peter Sin). 
March 1  9  4:05 – 4:55  LIT 368  Felix Gotti 
A question by Gilmer on the Atomicity of Monoid Domains ABSTRACT: Let $M$ be a commutative cancellative monoid, and let $R$ be an integral domain. The question of whether the monoid domain $R[x;M]$ is atomic provided that both $M$ and $R$ are atomic dates back to the 1980’s. In 1993, Roitman gave a negative answer to the question for $M = \nn_0$: he constructed an atomic integral domain $R$ such that the polynomial ring $R[x]$ is not atomic. However, the question of whether a monoid algebra $F[x;M]$ over a field $F$ is atomic provided that $M$ is atomic has been open since then. Here I will discuss a negative answer to this question when the field $F$ has finite characteristic. 
March 8  9  4:05 – 4:55  LIT 368  No seminar  Spring break 
March 15  9  4:05 – 4:55  LIT 368  Alexander York  A Structure Theorem for QuasiGorenstein Modules
Abstract: Let R be a CohenMacaulay factorial domain. An Rmodule M is quasiGorenstein if the projective dimension of M is equal to the grade of M and Ext_R^pd(M)(M,R) is isomorphic to M. An example of such a module is the critical group of a finite graph. We will show that this definition allows for us to give a structure theorem for quasiGorenstein Rmodules of projective dimension 1 related to the diagonalizability of matrices composed of entries in R which is an extension of the structure theorem for modules over a PID. This is accomplished by defining a certain type of filtration of Rmodules by quasiGorenstein modules allowing us to prove the splitting of a certain short exact sequence.

March 22  9  4:05 – 4:55  LIT 368  No seminar  this week 
March 29  9  4:05 – 4:55  LIT 368  No seminar  this week 
April 5  9  4:05 – 4:55  LIT 368  Marly Cormar  Atomicity of cyclic rational semirings
Abstract. Every subsemiring of the field Q that is not a ring (i.e., a rational semiring) is contained in the nonnegative cone of Q. The rational semiring S r generated by a given positive rational r (i.e., the cyclic rational semiring generated by r) is atomic as an additive monoid unless r = 1/n for some n ∈ N. Thus, “almost all” cyclic rational semirings are atomic monoids. I will present some of the most relevant atomic and factorization properties of the cyclic rational semirings. 
April 12  9  4:05 – 4:55  LIT 368  Kevin Keating  Heights of power series in characteristic p
Abstract: Let k be a perfect field of characteristic p. The set of all series of the form f(x)=x+a_1x^2+a_2x^3+… with a_i in k forms a group with the operation of composition, known as the Nottingham group of k. In this talk we consider several possible definitions for the height of such a series. These definitions are motivated by the definition of the height of a formal group law. 
April 22  9  4:05 – 4:55  LIT 368  Tiep  Sylow subgroups and character tables
Abstract. What information about Sylow psubgroups of a finite group can be read off from its character table? This problem was stated by Richard Brauer in his famous 1963 list, and has also received considerable attention because of its connections to the more recent GaloisMcKay conjecture. We will discuss various results on this problem, many of which are joint with Gabriel Navarro. 
Fall 2018
Date 
Period

Time

Location

Speaker

Topic


October 26  9  4:05 – 4:55  LIT 368  A. Turull  An invariant for ordinary characters arising from modular characters 
November 2  9  4:05 – 4:55  LIT 368  No seminar  Homecoming 
November 9  9  4:05 – 4:55  LIT 368  Raghu Pantangi 
Critical groups of van LintSchrijver cyclotomic Strongly Regular Graphs.
Abstract:
The critical group of a finite connected graph is an abelian group defined by the Smith normal form of its Laplacian. Let $K$ be a finite field and $D$ be subgroup of the multiplicative group. A cyclotomic Strongly Regular Graph is a Cayley graph on $(K,+)$ with ”connection” set $D$ that is Strongly regular. We will describe the critical groups of a family of cyclotomic SRG’s discovered by van Lint and Schrijver.

November 16  9  4:05 – 4:55  LIT 368  Felix Gotti  On monoid algebras with rational exponents 
November 23  9  4:05 – 4:55  LIT 368  No seminar  Thanksgiving 
November 30  9  4:05 – 4:55  LIT 368  Hossein Shahrtash  The implications of rational class sizes for the structure of a finite group 
Spring 2018
Date 
Period

Time

Location

Speaker

Topic


January 26  9  4:05 – 4:55  LIT 305  No seminar  Colloquium talk 
February 2  9  4:05 – 4:55  LIT 305  No seminar  Colloquium talk 
February 9  9  4:05 – 4:55  LIT 305  No seminar  Colloquium talk 
February 16  9  4:05 – 4:55  LIT 305  Tom Wolf  Automorphism Towers and subnormal series 
February 23  9  4:05 – 4:55  LIT 305  Tom Wolf  Automorphism Towers and subnormal series, cont 
March 2  9  4:05 – 4:55  LIT 305  Tom Wolf  Coprime actions and invariant Hall subgroups 
March 9  9  4:05 – 4:55  LIT 305  No seminar  Spring break 
March 16  9  4:05 – 4:55  LIT 305  No seminar  This week 
March 23  9  4:05 – 4:55  LIT 305  No seminar  This week 
March 30  9  4:05 – 4:55  LIT 339 The Atrium  Hossein Shahrtash  Rational class sizes and their implications about the structure of a finite group 
April 6  9  4:05 – 4:55  LIT 305  No seminar  This week 
April 13  9  4:05 – 4:55  LIT 305  Alexandre Turull  The invariant of a character 
April 20  9  4:05 – 4:55  LIT 305  Kevin Keating  The Artin character of a local field extension 
Fall 2017
Date 
Period

Time

Location

Speaker

Topic


September 1  9  4:05 – 4:55  LIT 368  Alexandre Turull  Dade’s conjectures and related conjectures, I 
September 8  9  4:05 – 4:55  LIT 368  No seminar  Hurricane Irma 
September 15  9  4:05 – 4:55  LIT 368  Alexandre Turull  Dade’s conjectures and related conjectures, II 
September 22  9  4:05 – 4:55  LIT 368  Peter Sin  ErdősKoRado problems for permutation groups 
September 29  9  4:05 – 4:55  LIT 368  Peter Sin  EKR for PSL(2,q) acting on the projective line 
October 6  9  4:05 – 4:55  LIT 368  No seminar  Homecoming 
October 13  9  4:05 – 4:55  LIT 368  Peter Sin  EKR for PSL(2,q) acting on the projective line (continued) 
October 20  9  4:05 – 4:55  LIT 368  No seminar  This week 
October 27  9  4:05 – 4:55  LIT 368  No seminar  This week 
November 3  9  4:05 – 4:55  LIT 368  Richard Crew  Fisocrystals, Weil groups and local class field theory 
November 10  9  4:05 – 4:55  LIT 368  No seminar  This week 
November 17  9  4:05 – 4:55  LIT 368  Richard Crew  Fisocrystals, Weil groups and local class field theory, cont. 
November 24  9  4:05 – 4:55  LIT 368  No seminar  Thanksgiving 
December 1  9  4:05 – 4:55  LIT 368  Kevin Keating  What are the padic numbers? 
Spring 2017
Date 
Period

Time

Location

Speaker

Topic


February 10  9  4:05 – 4:55  LIT 368  Tom Wolf  Regular orbits 
February 17  9  4:05 – 4:55  LIT 368  Tom Wolf  Regular orbits (continued) 
February 24  9  4:05 – 4:55  LIT 368  Pantangi  Smith group and Critical group of the Symplectic polar graph.
Abstract: The Smith group and Critical group are interesting invariants of a graph. The Smith group a graph is the cokernel of it’s adjacency matrix. The critical group a graph is a finite Abelian group whose order is the number of spanning forests of the graph. In this presentation, we will focus on some elementary linear algebra techniques that give us partial information about the Smith group and Critical group of a Strongly regular graph. We will also apply these techniques and some representation theory to find the Smith group and Critical group of the Symplectic Polar graph. 
March 3  9  4:05 – 4:55  LIT 368  Cyr  Semipermutability of subgroups in some simple groups 
March 10  9  4:05 – 4:55  LIT 368  No seminar  Spring Break 
March 17  9  4:05 – 4:55  LIT 368  Kevin Keating  What is a Hopf Algebra? 
March 24  9  4:05 – 4:55  LIT 368  Kevin Keating  Affine group schemes 
March 31  9  4:05 – 4:55  LIT 368  Kevin Keating  Affine Group Schemes II 
April 7  9  4:05 – 4:55  LIT 368  Kevin Keating  HopfGalois Extensions 
April 14  9  4:05 – 4:55  LIT 368  Yong Yang  On $p$parts of character degrees of finite groups
Abstract: Let $G$ be a finite group and $\Irr(G)$ the set of irreducible complex characters of $G$. Let $e_p(G)$ be the largest integer such that $p^{e_p(G)}$ divides $\chi(1)$ for some $\chi \in \Irr(G)$. In this talk, we show that $G:F(G)_p \leq p^{K e_p(G)}$ for a universal constant $K$. This settles a conjecture of A. Moreto. 
Fall 2016
Date 
Period

Time

Location

Speaker

Topic


October 17  9  4:05 – 4:55  LIT 368  Alexandre Turull  Maximal Subgroups of Finite Groups
Abstract: 
October 24  9  4:05 – 4:55  LIT 368  No seminar  Because of colloquium talk 
October 31  9  4:05 – 4:55  LIT 368  Alexandre Turull  Maximal Subgroups of Finite Groups, II 
November 7  9  4:05 – 4:55  LIT 368  No seminar  Because of colloquium talk 
November 14  9  4:05 – 4:55  LIT 368  Alexandre Turull  Maximal Subgroups of Finite Groups, III 
November 21  9  4:05 – 4:55  LIT 368  No Seminar  This week 
November 28  9  4:05 – 4:55  LIT 368  Alexandre Turull  Small orbits and regular orbits
Abstract: 
December 5  9  4:05 – 4:55  LIT 368  Alexandre Turull  Small orbits and regular orbits, II 
Spring 2016
Date 
Period

Time

Location

Speaker

Topic


February 5  7  1:55 – 2:45  LIT 305  Alexandre Turull  Characters of Finite Groups
Abstract: 
February 12  7  1:55 – 2:45  LIT 305  Alexandre Turull  Characters of Finite Groups
Abstract: 
February 19  7  1:55 – 2:45  LIT 305  Tom Wolf  More character theory 
February 26  7  1:55 – 2:45  LIT 305  Tom Wolf  More character theory 
March 4  7  1:55 – 2:45  LIT 305  No seminar  Spring Break 
March 11  7  1:55 – 2:45  LIT 305  Alexandre Turull  The Strengthened Dade Projective Conjecture
The Dade Projective Conjecture relates the existences of certain characters for the normalizers of chains of psubgroups of a finite group. This conjecture has been strengthened to include information about the p’part of their degrees, the fields of definition and the Schur indices. We will discuss a proof of this strengthened conjecture for the all the finite psolvable groups. 
March 18  7  1:55 – 2:45  LIT 305  Alexandre Turull  The Strengthened Dade Projective Conjecture II
This will continue the material discussed the previous week. 
March 25  7  1:55 – 2:45  LIT 305  Shahrtash  Recognizing direct products from their conjugate type vector 
March 28 (Monday)  9  4:05 – 4:55  LIT 368  Qing Xiang  A Linear Analogue of Kneser’s Theorem and Related Problems Abstract 
April 8  7  1:55 – 2:45  LIT 305  Kevin Keating  Galois Modules and Ramification Theory 
April 15  7  1:55 – 2:45  LIT 305  Kevin Keating  Galois Modules and Ramification Theory (continued) 
April 22  7  1:55 – 2:45  LIT 305  Josh Ducey  Critical groups of strongly regular graphs
Abstract: An active line of research has been to calculate the critical group for various families of graphs. In this talk we illustrate how to obtain partial information about the critical group of any strongly regular graph. Other methods that can be used to gain further insight will be illustrated through several examples. 
Spring 2015
Date 
Period

Time

Location

Speaker

Topic


January 27  9  4:05 – 4:55  LIT 305  Alexandre Turull  Endoisomorphisms
Abstract: 
February 3  9  4:05 – 4:55  LIT 305  Alexandre Turull  Endoisomorphisms
Abstract: 
February 10  9  4:05 – 4:55  LIT 305  Peter Sin  Title: Representations of the alternating group which are irreducible over subgroups.
Abstract: 
February 17  9  4:05 – 4:55  LIT 305  Kevin Keating  Trace, Norm, Etc. 
February 24  9  4:05 – 4:55  LIT 305  Tom Wolf  The GlaubermanIsaacs Correspondence 
March 3  9  4:05 – 4:55  LIT 305  No seminar  Spring Break 
March 10  9  4:05 – 4:55  LIT 305  Richard Crew  FIsocrystals and division algebras 
March 17  9  4:05 – 4:55  LIT 305  Liz Wiggins  Some Weyl modules for simple algebraic groups
Abstract: 
March 24  9  4:05 – 4:55  LIT 305  No seminar  this week 
March 31  9  4:05 – 4:55  LIT 305  No seminar  this week 
April 7  9  4:05 – 4:55  LIT 305  Peter Sin  The Smith group of the Hypercube graph.
Abstract. The hypercube graph is a basic example, closely related to the Hamming association scheme, which in turn plays an important role in coding theory. This talk is about the recent calculation of the Smith group of the hypercube, or equivalently the Smith Normal Form of its adjacency matrix. (Joint work with D. Chandler and Q. Xiang.) 
April 14  9  4:05 – 4:55  LIT 305  No seminar  this week 
Fall 2014
Date 
Period

Time

Location

Speaker

Topic


July 28  8  3:00 – 3:50  LIT 368  Pham Tiep  Nilpotent Hall and abelian Hall subgroups Abstract: To which extent can one generalize the Sylow theorems? One possible direction is to assume the existence of a nilpotent subgroup whose order and index are coprime. We will discuss recent joint work with various collaborators that gives a criterion to detect the existence of such subgroups in any finite group. 
September 12  9  4:05 – 4:55  LIT 368  Alexandre Turull  Generalizations of Jordan’s Theorem 
September 19  9  4:05 – 4:55  LIT 368  Peter Sin  Some remarks on Veronese and Grassmann varieties in characteristic 2 
September 26  9  4:05 – 4:55  LIT 368  Alexandre Turull  The GlaubermanIsaacs character correspondence and its inverse 
October 3  9  4:05 – 4:55  LIT 368  Doug Brozovic  An introduction to sharp permutation groups Abstract 
October 10  9  4:05 – 4:55  LIT 368  No seminar  this week 
October 17  9  4:05 – 4:55  LIT 368  No seminar  Homecoming 
October 24  9  4:05 – 4:55  LIT 368  Christopher Cyr  Title: A Theorem of Isaacs on SSemipermutable Subgroups and Some Consequences
Abstract: The familiar notion of a permutable subgroup can be generalized in many ways, one of which is Ssemipermutability. In recent years many authors have explored what can be said about a group when many subgroups satisfy a particular permutability condition. In this talk, we present a recent theorem of Isaacs concerning the normal closure of an Ssemipermutable subgroup H of a finite group G. In addition to proving the theorem, we mention some corollaries which result from considering the special cases where H is a Sylow psubgroup or a Hall πsubgroup of G. 
October 31  9  4:05 – 4:55  LIT 368  Alexander Gruber  Title: Design and Cryptanalysis of MatsumotoImai and its Variants
Abstract: The MatsumotoImai (MI) Cryptosystem was proposed in 1988 as a candidate for the national cryptosystem of the Japanese government. The MI scheme exploits the difficulty of determining the hidden structure of a finite field extension, promising similar security to RSA, yet with much faster encryption and decryption speeds. MI was broken in 1995 with an algebraic attack published by Jacques Patarin; however, there are several proposed improvements that offer increased security. In this talk, we outline the MI scheme, discuss its cryptanalysis, and 
November 7  9  4:05 – 4:55  LIT 368  Venkata Raghu Tej Pantangi  Title: Introduction to symmetric functions
Abstract: Let $X$ be a set of variables indexed by the natural numbers. A symmetric function $f$ is an element of $\mathbb{Q}[[X]]$ which is invariant under any permutation of $X$ and the degrees of monomials involved in $f$ are bounded. One can also view them as the elements of the inverse limit of the rings of symmetric polynomials in finite number of variables, considered as graded rings. Any $\mathbb{Q}$basis of the ring of symmetric polynomials is indexed by partitions of natural numbers. We will see four important bases and the linear relations among these bases. The role played by symmetric functions in the character theory of symmetric groups will also be discussed. 
November 14  9  4:05 – 4:55  LIT 368  Yong Yang  Title: Orbits of group actions
Abstract: The idea of a group is the mathematical abstraction of the common notion of symmetry. Group actions allow the study of groups via their action on suitable sets (such as vector spaces) which models the ways they arise in the real world. Naturally, the information on the orbits induced by a group action is central to the understanding of the action. As in the case of Sylow’s theorems, a result on the orbits of a group action is often at the core of a seemingly unrelated problem. In this talk, we discuss some recent developments in this area, and address some open problems. 
November 21  9  4:05 – 4:55  LIT 368  No seminar  this week 
November 28  9  4:05 – 4:55  LIT 368  No seminar  Thanksgiving 
December 5  9  4:05 – 4:55  LIT 368  No seminar  this week 