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seminars:alge [2026/07/17 16:18] – xqiaoseminars:alge [2026/08/07 01:34] (current) – htongvie
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-**#####The Algebra Seminar#####**+**The Algebra Seminar**
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 [[https://binghamton.zoom.us/j/94820318435?pwd=csFLTKnx0MIwKgLCh9LqRphUn54usX.1 | Algebra Seminar Zoom Meeting Link]] [[https://binghamton.zoom.us/j/94820318435?pwd=csFLTKnx0MIwKgLCh9LqRphUn54usX.1 | Algebra Seminar Zoom Meeting Link]]
  
-Organizers: [[:people:alex:start|Alex Feingold]], [[:people:daniel:start|Daniel Studenmund]] and [[:people:tongviet:start|Hung Tong-Viet]]+Organizers: [[:people:alex:start|Alex Feingold]],  [[:people:mazur:start|Marcin Mazur]], [[:people:daniel:start|Daniel Studenmund]] and [[:people:tongviet:start|Hung Tong-Viet]]
  
 To receive announcements of seminar talks by email, please email one of the organizers with your name, email address and reason for joining this list if you are external to Binghamton University. To receive announcements of seminar talks by email, please email one of the organizers with your name, email address and reason for joining this list if you are external to Binghamton University.
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-=====Spring 2026=====+=====Fall 2026=====
  
-   * **January 20**\\  <html> <span style="color:blue;font-size:120%">Organizational Meeting</span></html> \\         \\  <WRAP center box 90%> Please think about giving a talk in the Algebra Seminar, or inviting an outside speaker.+   * **August 18**\\  <span style="color:blue;font-size:120%"> **Organizational Meeting **</span> \\         \\  <WRAP center box 90%> Please think about giving a talk in the Algebra Seminar, or inviting an outside speaker.
 </WRAP> </WRAP>
  
-   * **January 27**\\  <html> <span style="color:blue;font-size:120%"> Alex Feingold (Binghamton University) </span></html> \\      **//Tessellations from hyperplane families: Weyl and non-Weyl cases//** \\   \\  <WRAP center box 90%> **//Abstract//**: In collaboration with Robert Bieri and Daniel Studenmund, we have been studying tessellations of Euclidean spaces which arise from families of hyperplanes. A rich class of examples come from a finite type root system and associated finite Weyl group, W, whose affine extension acts on the tessellation. We have also seen examples which do not come from a root system and Weyl group, so we want to understand exactly what geometric properties of the hyperplane families are needed for our project. Our goal has been to define and study piecewise isometry groups acting on such tessellations. In this talk I will discuss the details of some Weyl and some non-Weyl tessellations.  </WRAP>+   * **August 25**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-   * **February 3**\\  <html> <span style="color:blue;font-size:120%"> Tim Riley (Cornell University) </span></html> \\      **//Conjugator length//** \\   \\  <WRAP center box 90%> **//Abstract//**: The conjugacy problem for a finitely generated group $G$ asks for an algorithm which, on input a pair of words u and v, declares whether or not they represent conjugate elements of $G$. The conjugator length function $CL$ is its most direct quantification: $CL(n)$ is the minimal $N$ such that if $u$ and $v$ represent conjugate elements of $G$ and the sum of their lengths is at most $n$, then there is a word $w$ of length at most $N$ such that $uw=wv$ in $G$.  I will talk about why this function is interesting and how it can behave, and I will highlight some open questions.  En route I will talk about results variously with Martin Bridson, Conan Gillis, and Andrew Sale, as well as recent advances by Conan Gillis and Francis Wagner. </WRAP> 
  
-    * **February 10**\\  <html> <span style="color:blue;font-size:120%"> Ryan McCulloch (Binghamton University) </span></html> \\      **//A p-group Classification Related to Density of Centralizer Subgroups//** \\   \\  <WRAP center box 90%> **//Abstract//**: If $\mathfrak{P}$ is a property pertaining to subgroups of a $p$-group $G$, and if each subgroup with property $\mathfrak{P}$ contains $Z(G)$, then a group $G$ whose subgroups are dense with respect to property $\mathfrak{P}$ must satisfy the following criteria:+  * **September 1**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-$|Z(G)|= p$ and every subgroup $H$ of order at least $p^2$ contains $Z(G)$.  +  * **September 8**\\  <html> <span style="color:blue;font-size:120%"> Monday classes meet</span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-I will discuss our progress in obtaining a classification of all such $p$-groups. This is joint work with Mark Lewis and Tae Young Lee. </WRAP> 
  
-   * **February 17**\\  <html> <span style="color:blue;font-size:120%"> Tae Young Lee (Binghamton University) </span></html> \\      **//Title: Finite groups with many elements of the same order//** \\   \\  <WRAP center box 90%> **//Abstract//**: It is a well-known fact that if more than 3/4 of the elements of a finite group are involutions then the group is abelian. Berkovich proved that if more than 4/15 are involutions then the group must be solvable. Motivated by these results, Deaconescu asked the following question: If at least half of the elements are of the same order, $k$, does the group have to be solvable? In this talk, we prove this when $k = p^a$ for primes $p$ except when $p = 2,3$ and $a > 1$, and give counterexamples for larger powers of 2 and 3 except $k = 4$, and also for several other types of composite numbers. We also show that when $k > 4$, it is always possible to find a non-solvable group such that at least 3/19 of its elements have order $k$. This is a joint work with Ryan McCulloch. </WRAP>+  * **September 15**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-   * **February 24**\\  <html> <span style="color:blue;font-size:120%"> Lei Chen (Bielefeld University, by Zoom) </span></html> \\      **//Covering a finite group by the conjugates of a coset//** \\   \\  <WRAP center box 90%> **//Abstract//**: It is well known that for a finite group G and a proper subgroup A of G, it is impossible to cover G with the conjugates of A. Thus, instead of the conjugates of A, we take the conjugates of the coset Ax in G and check if the union of $(Ax)^g$ covers G-{1} for g in G. Moreover, if $(Ax)^g$ covers G for all Ax in Cos(G:A), we say that (G,A) is CCI. We are aiming to classify all such pairs. It has been proven by Baumeister-Kaplan-Levy that this can be reduced to the case where A is maximal in G, and so that the action of G on Cos(G:A) is primitive, here Cos(G:A) stands for the set of right cosets of A in G. And they showed that (G,A) is CCI if G is 2-transitive. By O'Nan-Scott Theorem and CFSG (classification of finite simple groups), we see that G is either an affine group or almost simple. In the paper by Baumeister-Kaplan-Levy, it is shown that affine CCI groups are 2-transitive. Thus, it remains to consider the almost simple groups. By employing the knowledge of buildings, representation theory, and Aschbacher-Dynkin theorem, we prove that, apart from finitely many small cases, the CCI almost simple groups are 2-transitive.  </WRAP>+   * **September 22**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-   * **March 3**\\  <html> <span style="color:blue;font-size:120%"> Chaitanya Joglekar (Binghamton University) </span></html> \\      **//Lattice basis reduction and the LLL algorithm//** \\   \\  <WRAP center box 90%> **//Abstract//**: A lattice L is a subgroup of $\mathbb{R}^n$ isomorphic to $\mathbb{Z}^n$. Finding a vector in L of the shortest length has many applications in number theory, cryptography and optimisation. While finding a vector with the shortest length is an NP hard problem, the LLL algorithm finds a “short enough” vector in Polynomial time. 
-In this talk, we will go over the LLL algorithm and demonstrate one of its applications, finding a Diophantine approximation for a finite set of rational numbers. </WRAP> 
  
-   * **March 10**\\  <html> <span style="color:blue;font-size:120%"> Hanlim Jang (Binghamton University) </span></html> \\      **//Isoperimetric functions of nilpotent groups//** \\   \\  <WRAP center box 90%> **//Abstract//**: Isoperimetric functions are a measure of the efficiency of solving the word problem in a finitely presented group. In terms of the length of a word which is generated by generators of a finitely presented group, isoperimetric functions determine how many relators we need to apply at most in order to transform a reduced word to identity. In this talk, we will prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1. Our strategy will be using an induction argument on the class c. This talk is based on the paper Isoperimetric inequalities for nilpotent groups written by S.M Gersten, D. F. Holt, and T. R. Riley. +   * **September 29**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
  
- </WRAP>+   * **October 6**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-   * **March 17**\\  <html> <span style="color:blue;font-size:120%"> William Cocke (Carnegie Mellon University) </span></html> \\      **//Determining the Free Spectrum of $A_5$//** \\   \\  <WRAP center box 90%> **//Abstract//**: We determine the structure of the group of commutator word maps on the alternating group $A_5$. As a result obtain a formula for the size of the relatively free groups of finite rank in the variety generated by $A_5$. </WRAP> 
  
-   * **March 24**\\  <html> <span style="color:blue;font-size:120%">  No Meeting (No Speaker) </span></html> \\      +   * **October 13**\\  <html> <span style="color:blue;font-size:120%">  No class </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-   * **March 31**\\  <html> <span style="color:blue;font-size:120%">  No Meeting (Spring Break) </span></html> \\ +   * **October 20**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-   * **April 7**\\  <html> <span style="color:blue;font-size:120%"> No Meeting (Monday Classes Meet) </span></html>\\ 
  
-   * **April 14**\\  <html> <span style="color:blue;font-size:120%"> Luna Gal (Binghamton University) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP>+   * **October 27**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-   * **April 21**\\  <html> <span style="color:blue;font-size:120%"> Sean Cleary (City College of New York and Graduate Center of CUNY) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP> 
  
-   * **April 28**\\  <html> <span style="color:blue;font-size:120%"> Thi Hoai Thu Quan (Binghamton University) </span></html> \\      **// The construction of the Chevalley groups and their simplicity//** \\   \\  <WRAP center box 90%> **//Abstract//**: Most of the groups appearing in the classification of finite simple groups are the finite simple groups of Lie type. One way to construct these groups is through subgroups of the automorphism groups of the simple Lie algebras over finite fields; groups obtained in this way are called Chevalley groups.+   * **November 3**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
-In this talk, we describe this construction and the $(B,N)$-pair structure of a Chevalley group arising from it. We also explain how the $(B,N)$-pair structure can be used to prove the simplicity of certain Chevalley groups. </WRAP> 
  
-   * **May 5**\\  <html> <span style="color:blue;font-size:120%"> Nguyen N. Hung (University of Akron) </span></html> \\      **//The $p$-rationality of Deligne-Lusztig characters//** \\   \\  <WRAP center box 90%> **//Abstract//**: Deligne--Lusztig characters are virtual characters of finite reductive groups, constructed via $\ell$-adic cohomology of varieties associated with $F$-stable maximal tori. They provide a systematic framework for classifying, and often explicitly constructing, irreducible complex representations of these groups. In this talk, I will present a recent result showing that if a Deligne--Lusztig character has degree coprime to $p$, then its $p$-rationality coincides with that of the linear character of the maximal torus from which it is induced. I will also discuss evidence suggesting that, more generally, Lusztig induction preserves $p$-rationality for characters of $p'$-degree. </WRAP>+   * **November 10**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
  
 +   * **November 17**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
 +
 +   * **November 24**\\  <html> <span style="color:blue;font-size:120%">  Friday classes meet </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
 +
 +   * **December 1**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>
 +
 +   * **December 8**\\  <html> <span style="color:blue;font-size:120%">  Speaker (Binghamton University) </span></html> \\      **//Title //** \\   \\  <WRAP center box 90%> **//Abstract//**:  </WRAP>   
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   * [[seminars:alge:alge-Spring2025|Spring 2025]]   * [[seminars:alge:alge-Spring2025|Spring 2025]]
   * [[seminars:alge:alge-fall2025|Fall 2025]]   * [[seminars:alge:alge-fall2025|Fall 2025]]
 +  * [[seminars:alge:alge-Spring2026|Spring 2026]]
seminars/alge.1784305132.txt · Last modified: by xqiao