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--- seminars:alge [2024/01/27 13:51]
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+++ seminars:alge [2024/04/28 23:06] (current)
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-   * **January 30**\\ <html> <span style="color:blue;font-size:120%"> Dikran Karagueuzian (Binghamton University) </span></html> \\      **//Title TBA//** \\   \\  <WRAP center box 90%> **//Abstract//**: TBA
+   * **January 30**\\ <html> <span style="color:blue;font-size:120%"> Dikran Karagueuzian (Binghamton University) </span></html> \\      **//You Were Always Studying Cohomology//** \\  \\  <WRAP center box 90%> **//Abstract//**: We will discuss the observation that carrying, as taught in grade-school arithmetic, is a cohomology class.  This observation is something of a folk theorem.  It was surely known to Eilenberg and MacLane, but the earliest written record I can find is an internet post from the 90s by Dolan.
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-   * **February 6**\\ <html> <span style="color:blue;font-size:120%"> Daniel Studenmund (Binghamton University) </span></html> \\      **//Title TBA//** \\   \\  <WRAP center box 90%> **//Abstract//**: TBA
+   * **February 6**\\ <html> <span style="color:blue;font-size:120%"> Daniel Studenmund (Binghamton University) </span></html> \\      **//Finite generation of lattices and Kazhdan's Property (T)//** \\   \\  <WRAP center box 90%> **//Abstract//**: Lattices in semisimple Lie groups form an important and rich class of finitely generated infinite groups. But it is not immediately obvious from their definition that lattices are finitely generated. This was first proved for a large class of lattices by Kazhdan using a property now known as (T). In this expository talk I will introduce the definition of Property (T) and discuss its relationship to amenability and finite generation.
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-   * **February 13**\\ <html> <span style="color:blue;font-size:120%"> Hung Tong-Viet (Binghamton University) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract
+   * **February 13**\\ <html> <span style="color:blue;font-size:120%"> Hung Tong-Viet (Binghamton University) </span></html> \\      **//Conditional characterization of solvability and nilpotency of finite groups//** \\   \\  <WRAP center box 90%> **//Abstract//**: As a consequence of the classification of nonsolvable $N$-groups, Thompson proved in $1968$ that a finite group $G$ is solvable if and only if every two-generated subgroup of $G$ is solvable. Various extensions of this theorem have been obtained over the years. In this talk, I will survey some of these results and discuss new characterizations of finite solvable and nilpotent groups using certain restriction on the two-generated subgroups.  I will end the talk with applications to the solvable conjugacy class graph of groups.
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-   * **February 20**\\ <html> <span style="color:blue;font-size:120%"> ? ( University) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract
+   * **February 20**\\ <html> <span style="color:blue;font-size:120%"> No Meeting </span></html> \\
-</WRAP>
-   * **February 27**\\ <html> <span style="color:blue;font-size:120%"> ? ( University) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract
+   * **February 27**\\ <html> <span style="color:blue;font-size:120%"> No Meeting </span></html> \\
-</WRAP>
    * **March 5**\\  <html> <span style="color:blue;font-size:120%"> No Algebra Seminar - Spring Break </span></html> \\
-   * **March 12**\\ <html> <span style="color:blue;font-size:120%"> ? ( University) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract
+   * **March 12**\\ <html> <span style="color:blue;font-size:120%"> Inna Sysoeva (Binghamton University) </span></html> \\      **//Irreducible $n-$dimensional representations of the group of conjugating automorphisms of a free group on $n$ generators//** \\   \\  <WRAP center box 90%> **//Abstract//**: Let $F_n$ be the free group on $n$ generators $x_1, \dots ,x_n.$ The group of conjugating automorphisms $C_n$ is a subgroup of $Aut(F_n)$ consisting of those automorphisms which map every free group generator $x_i$ into a word of the form $W_i^{-1}( x_1 , \dots x_n)x_{\pi(i)} W_i( x_1 , \dots x_n),$ where $W_i( x_1 , \dots x_n)\in F_n$ and $\pi$ is some permutation of indices, $\pi\in S_n.$ The subgroup of $C_n$ that preserves the product $x_1\dots x_n$ is isomorphic to the braid group on $n$ strings, $B_n.$
-</WRAP>
-   * **March 19**\\ <html> <span style="color:blue;font-size:120%"> ? ( University) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract
-</WRAP>
-   * **March 26**\\ <html> <span style="color:blue;font-size:120%"> Andrew Velasquez-Berroteran (Binghamton University) </span></html> \\      **//Title TBA//** \\   \\  <WRAP center box 90%> **//Abstract//**: TBA
+In this talk I am going to describe my new results on the extensions of the irreducible $n-$dimensional representations of the braid group $B_n$ to the group of conjugating automorphisms $C_n$ of a free group $F_n.$ I will cover all relevant background material on the above-mentioned groups and their representations, so no previous knowledge of the subject is expected.
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-   * **April 2**\\ <html> <span style="color:blue;font-size:120%"> Omar Saldarriaga (Highpoint University) </span></html> \\      **//Title TBA//** \\   \\  <WRAP center box 90%> **//Abstract//**: TBA
+   * **March 19**\\ <html> <span style="color:blue;font-size:120%"> No Meeting </span></html> \\
+   * **March 26**\\ <html> <span style="color:blue;font-size:120%"> No Meeting </span></html> \\
+   * **April 2**\\ <html> <span style="color:blue;font-size:120%"> Omar Saldarriaga (Highpoint University) presented on Zoom </span></html> \\      **//The Lie algebra of the transformation group of certain affine homogeneous manifolds//** \\   \\  <WRAP center box 90%> **//Abstract//**: In this talk we will show that, under certain algebraic conditions, a bi-invariant linear connection $\nabla^+$ on a Lie group $G$ induces an invariant linear connection $\nabla$ on a homogeneous space $G/H$ so that the projection $\pi:G\to G/H$ is an affine map. We will also show that if the subgroup $H$ is discrete, there is a method to compute the Lie algebra of the group of affine transformations of $G/H$ preserving the connection $\nabla$. As an application, we will exhibit the Lie algebra of the group of affine transformations of the orientable flat affine surfaces.
 </WRAP>
-   * **April 9**\\ <html> <span style="color:blue;font-size:120%"> ? ( University) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract
+   * **April 9**\\ <html> <span style="color:blue;font-size:120%"> Luna Elliott (Binghamton University) </span></html> \\      **//How semigroup people think about (inverse) semigroups//** \\   \\  <WRAP center box 90%> **//Abstract//**: I will give a beginner friendly introduction to semigroups, inverse semigroups and the concepts which are well-known and heavily used by people in these areas. These include green's relations free objects, wagner-preston and special subclasses of these objects. I'm very open to going on tangents if people want me to talk more about anything in particular.
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-   * **April 16**\\ <html> <span style="color:blue;font-size:120%"> ? Rachel Skipper (University of Utah) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract
+   * **April 16**\\ <html> <span style="color:blue;font-size:120%"> Rachel Skipper (University of Utah) </span></html> \\      **//Computing Scale in Neretin's group//** \\   \\  <WRAP center box 90%> **//Abstract//**: For an automorphism of a totally disconnected, locally compact (tdlc) group, Willis introduced the notion of scale which arose in the development of the general theory of these groups. In this talk, we will discuss the setting where the tdlc group is Neretin's group and where the automorphism comes from conjugation in the group. This is an ongoing joint work with Michal Ferov and George Willis at the University of Newcastle.
 </WRAP>
    * **April 23**\\  <html> <span style="color:blue;font-size:120%"> No Algebra Seminar - Passover Break </span></html> \\
-   * **April 30**\\ <html> <span style="color:blue;font-size:120%"> ? ( University) </span></html> \\      **//Title//** \\   \\  <WRAP center box 90%> **//Abstract//**: Text of Abstract
+   * **April 30**\\ <html> <span style="color:blue;font-size:120%"> Andrew Velasquez-Berroteran (Binghamton University) </span></html> \\      **//Neuroscience: An Algebraic and Topological Viewpoint//** \\   \\  <WRAP center box 90%> **//Abstract//**: Neuroscience is the study of the nervous system, and one popular aspect of the nervous system is the brain. Many fields of mathematics have contributed to neuroscience research which include but are not limited to statistics, partial differential equations, dynamics and mathematical physics, etc.
+In this talk, I will talk about a brief overview of how algebra and topology has recently been used in the study of the brain. We will primarily be looking at neural coding, and at the end talk about what’s known as the neural ring and neural ideal. I will present under the assumption that attendees will have basic ring theory and  topology knowledge but no background knowledge in neuroscience.
 </WRAP>

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