seminars:alge
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seminars:alge [2025/04/30 16:47] daniel |
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| - | **The seminar will meet in-person on Tuesdays in room WH-100E at 2:50 p.m. There should be refreshments served at 4:00 in room WH-102. Masks are optional.** | + | **The seminar will meet in-person on Tuesdays in room WH-100E at 2:45 p.m. There should be refreshments served at 3:45 in our new lounge/coffee room, WH-104. Masks are optional.** |
| **Anyone wishing to give a talk in the Algebra Seminar this semester is requested to contact the organizers at least one week ahead of time, to provide a title and abstract. If a speaker prefers to give a zoom talk, the organizers will need to be notified at least one week ahead of time, and a link will be posted on this page.** | **Anyone wishing to give a talk in the Algebra Seminar this semester is requested to contact the organizers at least one week ahead of time, to provide a title and abstract. If a speaker prefers to give a zoom talk, the organizers will need to be notified at least one week ahead of time, and a link will be posted on this page.** | ||
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| - | =====Spring 2025===== | + | =====Fall 2025===== |
| - | * **January 21**\\ <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 19**\\ <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. |
| </WRAP> | </WRAP> | ||
| - | * **January 28**\\ <html> <span style="color:blue;font-size:120%"> Daniel Studenmund (Binghamton University) </span></html> \\ **//Piecewise isometry groups arising from Weyl groups//** \\ \\ <WRAP center box 90%> **//Abstract//**: Here’s a fun way to build a group by cutting and pasting: Start with a Euclidean, spherical, or hyperbolic model geometry $X$ carrying a collection $\mathcal{H}$ of totally geodesic codimension-1 submanifolds determining a regular tessellation $\Delta$ of $X$. A piecewise isometry of $\Delta$ is defined by cutting out finitely many subspaces $S_1,\dotsc, S_k \in \mathcal{H}$ and isometrically mapping the components of what remains to the components obtained by cutting out another finite collection of subspaces $T_1,\dotsc, T_k \in \mathcal{H}$. The collection of all piecewise isometries is a group $PI(\Delta)$. When $\Delta$ is a tessellation of $\mathbb{R}$ by isometric line segments, $PI(\Delta)$ is an extension of Houghton’s group $H_2$. When $\Delta$ is a tessellation of the hyperbolic plane by ideal triangles, $PI(\Delta)$ naturally extends Thompson’s group $V$. Bieri and Sach studied $PI(\mathbb{Z}^n)$, where $\mathbb{Z}^n$ is the standard tessellation of Euclidean space by isometric cubes, obtaining lower bounds on their finiteness lengths and presenting a careful analysis of their normal subgroup structure. | + | * **August 26**\\ <html> <span style="color:blue;font-size:120%"> Ryan McCulloch (Binghamton University) </span></html> \\ **//The commuting graph and the centralizer graph of a group//** \\ \\ <WRAP center box 90%> **//Abstract//**: Let $G$ be a group. The commuting graph $\mathfrak{C}(G)$ for $G$ is the graph whose vertices are $G-Z(G)$ and if $a, b \in G-Z(G)$, $a \neq b$, then there is an edge between $a$ and $b$ if $ab = ba$. A close cousin of $\mathfrak{C}(G)$ is the centralizer graph, which we define. When a connected component of $\mathfrak{C}(G)$ is a complete graph, the corresponding component in the centralizer graph is an isolated vertex, and we call such a component trivial. Otherwise, the natural bijection between the commuting graph and the centralizer graph preserves the diameter of connected components. |
| - | Our story will start with the piecewise isometry group of the tessellation of the Euclidean plane by equilateral triangles, and generalize to piecewise isometry groups of Euclidean tessellations associated with affine Weyl groups of type $A_n$. Pictures will be drawn and preliminary results on algebraic structure and finiteness properties will be discussed. Time permitting, we will connect our discussion to the tessellation of hyperbolic 3-space by regular ideal tetrahedra. This talk covers work in progress with Robert Bieri and Alex Feingold. | + | One sees that if $G$ is a Frobenius group with a nonabelian kernel and a nonabelian complement where the complement has nontrivial center, then the centralizer graph of $G$ has more than one nontrivial component. Can this happen in a $p$-group? The answer is yes! In fact, for any specified number $k$ of nontrivial components and any diameter sizes $n_1,\dots, n_k$, one can construct a $p$-group of nilpotency class 2 whose centralizer graph has these specs. This is joint work with Mark Lewis. </WRAP> |
| - | </WRAP> | + | |
| - | * **February 4**\\ <html> <span style="color:blue;font-size:120%"> Dikran Karagueuzian (Binghamton University) </span></html> \\ **//You Need a Yoneda//** \\ \\ <WRAP center box 90%> **//Abstract//**: The Yoneda Lemma is widely regarded as the most-commonly-quoted result of category theory. This (expository) talk will discuss instances of the lemma appearing in the undergraduate mathematics curriculum, particularly linear algebra. | + | * **September 2**\\ <html> <span style="color:blue;font-size:120%"> No Meeting (Monday classes meet) </span></html> \\ |
| - | </WRAP> | + | |
| - | * **February 11**\\ <html> <span style="color:blue;font-size:120%"> Hung Tong-Viet (Binghamton University) </span></html> \\ **//Orders of commutators in finite groups//** \\ \\ <WRAP center box 90%> **//Abstract//**: In this talk, I will discuss some problems concerning the orders of some commutators in finite groups and how they affect the structure of the group. | + | * **September 9**\\ <html> <span style="color:blue;font-size:120%"> Chris Schroeder (Binghamton University) </span></html> \\ **//A topological quantum field theory and invariants of finite groups//** \\ \\ <WRAP center box 90%> **//Abstract//**: In this talk, we will discuss the properties of finite groups that are witnessed by the group invariants arising in the context of Dijkgraaf-Witten theory, a topological quantum field theory, as invariants of surfaces. Assuming the theory is derived from the complex group algebra of a finite group, these invariants are generalizations of the commuting probability, an invariant that has been well studied in the literature. The main goal of this talk is to construct these invariants from scratch, assuming no previous knowledge of quantum mechanics. </WRAP> |
| - | </WRAP> | + | |
| - | * **February 18**\\ <html> <span style="color:blue;font-size:120%"> No Speaker, No Meeting </span></html> \\ | + | * **September 16**\\ <html> <span style="color:blue;font-size:120%"> Alex Feingold (Binghamton University) </span></html> \\ **//Lie Algebras, Representations, Roots, Weights, Weyl groups and Clifford Algebras//** \\ \\ <WRAP center box 90%> **//Abstract//**: Lie algebras and their representations have been well-studied and have applications in mathematics and physics. The classification of finite dimensional Lie algebras over **C** by Killing and Cartan inspired the classification of finite simple groups. Geometry and combinatorics are both involved through root and weight systems of representations, with the Weyl group of symmetries playing a vital role. Infinite dimensional Kac-Moody Lie algebras have deeply enriched the subject and connected with string theory and conformal field theory. In a collaboration with Robert Bieri and Daniel Studenmund, we have been studying tessellations of Euclidean and hyperbolic spaces which arise from the action of affine and hyperbolic Weyl groups. Our goal has been to define and study piecewise isometry groups acting on such tessellations. |
| - | * **February 25**\\ <html> <span style="color:blue;font-size:120%"> No Speaker, No Meeting </span></html> \\ | + | Today I will present background material on Lie algebras, representations and examples which show the essential structures. I will present a construction of representations of the orthogonal Lie algebras, $so(2n,F)$, of type |
| + | $D_n$ as matrices and also using Clifford algebras to get spinor representations. | ||
| + | </WRAP> | ||
| - | * **March 4**\\ <html> <span style="color:blue;font-size:120%"> Thu Quan (Binghamton University) </span></html> \\ **//Squaring a conjugacy class in a finite group//** \\ \\ <WRAP center box 90%> **//Abstract//**: Let $G$ be a finite group and $K$ be a conjugacy class of $G$. Then $K^2$ consists of the products of any two elements in $K$. In this talk, we consider some equivalent conditions for $K^2$ to be a conjugacy class of $G$. This talk is based on the paper by Guralnick and Navarro in 2015. | + | * **September 23**\\ <html> <span style="color:blue;font-size:120%"> No Algebra Seminar </span></html> \\ |
| - | </WRAP> | + | |
| - | * **March 11**\\ <html> <span style="color:blue;font-size:120%"> No Meeting, Spring Break </span></html> \\ | + | * **September 30**\\ <html> <span style="color:blue;font-size:120%"> Thu Quan (Binghamton University) </span></html> \\ **//A generalization of Camina pairs and orders of elements in cosets//** \\ \\ <WRAP center box 90%> **//Abstract//**: Let $G$ be a finite group with a nontrivial proper subgroup $H$. If $H$ is normal in $G$ and for every element $x\in G\setminus H$, $x$ is conjugate to $xh$ for all $h\in H$, then the pair $(G,H)$ is called a Camina pair. In 1992, Kuisch and van der Waall proved that $(G,H)$ is a Camina pair if and only if every nontrivial irreducible character of $H$ induces homogeneously to $G$. In this talk, we discuss the equivalence of these two conditions on the pair $(G,H)$ without assuming that $H$ is normal in $G$. Furthermore, we determine the structure of $H$ under the hypothesis that, for every element $x\in G\setminus H$ of odd order, all elements in the coset $xH$ also have odd order. </WRAP> |
| - | * **March 18**\\ <html> <span style="color:blue;font-size:120%"> James Hyde (Binghamton University) </span></html> \\ **//Small generating sets for groups of homeomorphisms of the Cantor set//** \\ \\ <WRAP center box 90%> **//Abstract//**: I will give the definition of Chabauty's space of marked groups and use it to give a nicer proof of a result from my thesis. I will then discuss joint work with Collin Bleak, Casey Donoven, Scott Harper on stronger notions of small generating sets for groups of homeomorphisms of the Cantor set. | + | * **October 7**\\ <html> <span style="color:blue;font-size:120%"> No Algebra Seminar </span></html> \\ |
| - | </WRAP> | + | |
| - | * **March 25**\\ <html> <span style="color:blue;font-size:120%"> Chris Schroeder (Binghamton University) </span></html> \\ **//Finite groups whose maximal subgroups have almost odd index //** \\ \\ <WRAP center box 90%> **//Abstract//**: A recurring theme in finite group theory is understanding how the structure of a finite group is determined by the arithmetic properties of group invariants. There are results in the literature determining the structure of finite groups whose irreducible character degrees, conjugacy class sizes or indices of maximal subgroups are odd. These results have been extended to include those finite groups whose character degrees or conjugacy class sizes are not divisible by 4. In this paper, we determine the structure of finite groups whose maximal subgroups have index not divisible by 4. As a consequence, we obtain some new 2-nilpotency criteria. This is joint work with Prof. Hung Tong-Viet. | + | * **October 14**\\ <html> <span style="color:blue;font-size:120%"> Hung Tong-Viet (Binghamton University) </span></html> \\ **//Orders of commutators and Products of conjugacy classes in finite groups//** \\ \\ <WRAP center box 90%> **//Abstract//**: Let $G$ be a finite group, $x\in G$, and let $p$ be a prime. In this talk, we explore conditions that forces $x$ to lie in certain characteristic subgroups of $G$. In particular, we prove that the commutator $[x,g]$ is a $p$-element for all $g\in G$ if and only if $x$ is central modulo $O_p(G)$, the largest normal $p$-subgroup of $G$. This result unifies and generalizes aspects of both the Baer-Suzuki theorem and Glauberman's $Z_p^*$-theorem. Additionally, we show that if $x\in G$ is a $p$-element and there exists an integer $m\ge 1$ such that for every $g\in G$, the commutator $[x,g]$ is either trivial or has order $m$, then the subgroup generated by the conjugacy class of $x$ is solvable. As an application, we confirm a conjecture of Beltran, Felipe, and Melchor: if $K$ is a conjugacy class in $G$ such that the product $K^{-1}K=1\cup D\cup D^{-1}$ for some conjugacy class $D$, then the subgroup generated by $K$ is solvable. </WRAP> |
| - | </WRAP> | + | |
| - | * **April 1**\\ <html> <span style="color:blue;font-size:120%"> Andrew Velasquez-Berroteran (Binghamton University) </span></html> \\ **//Coverings of Groups and Rings//** \\ \\ <WRAP center box 90%> **//Abstract//**: Given a group G, a covering of G is a collection of proper subgroups of G whose set-theoretic union is G. | + | * **October 21**\\ <html> <span style="color:blue;font-size:120%"> Inna Sysoeva (Binghamton University) </span></html> \\ **//Title//** \\ \\ <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP> |
| - | The first part of my talk will be dedicated to some history of coverings of groups and providing some results on which finite groups have an equal covering, which is a type of covering where each subgroup is of the same order. | + | |
| - | The second part of my talk will be dedicated to extending the notion of coverings of groups to that of rings. One result of this extension is determining necessary conditions for a ring $R$ so that the ring of polynomials R[X] has a special type of covering. | + | |
| - | </WRAP> | + | |
| - | * **April 8**\\ <html> <span style="color:blue;font-size:120%"> Edgar A Bering IV (San Jose State University) </span></html> \\ **//Two-generator subgroups of free-by-cyclic groups//** \\ \\ <WRAP center box 90%> **//Abstract//**: In general, the classification of finitely generated subgroups of a given group is intractable. Even restricting to two-generator subgroups is not enough. However, in a geometric setting classification is possible. For example, a two-generator subgroup of a right-angled Artin group is either free or free abelian. Jaco and Shalen proved that a two-generator subgroup of the fundamental group of an orientable atoroidal irreducible 3-manifold is either free, free-abelian, or finite-index. In this talk I will present recent work proving a similar classification theorem for two generator mapping-torus groups of free group endomorphisms: every two generator subgroup is either free or conjugate to a sub-mapping-torus group. As an application we obtain an analog of the Jaco-Shalen result for free-by-cyclic groups with fully irreducible atoroidal monodromy. While the statement is algebraic, the proof technique uses the topology of finite graphs, a la Stallings. This is joint work with Naomi Andrew, Ilya Kapovich, and Stefano Vidussi. | + | * **October 28**\\ <html> <span style="color:blue;font-size:120%"> Daniel Studenmund (Binghamton University) </span></html> \\ **//Title//** \\ \\ <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP> |
| - | </WRAP> | + | * **November 4**\\ <html> <span style="color:blue;font-size:120%"> Robert Bieri (Binghamton University) </span></html> \\ **//Title//** \\ \\ <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP> |
| - | * **April 15**\\ <html> <span style="color:blue;font-size:120%"> No Algebra Seminar </span></html> \\ | + | * **November 11**\\ <html> <span style="color:blue;font-size:120%"> Tae Young Lee (Binghamton University) </span></html> \\ **//Title//** \\ \\ <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP> |
| - | * **April 22**\\ <html> <span style="color:blue;font-size:120%"> No Algebra Seminar - Monday Classes Meet </span></html> \\ | + | * **November 18**\\ <html> <span style="color:blue;font-size:120%"> Nguyen N. Hung (University of Akron) </span></html> \\ **//Title//** \\ \\ <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP> |
| - | * **April 29**\\ <html> <span style="color:blue;font-size:120%"> Hanlim Jang (Binghamton University) </span></html> \\ **//Dehn function and the van Kampen diagram//** \\ \\ <WRAP center box 90%> **//Abstract//**: Historically, the word problem leads to the definition of the Dehn function which measures the difficulty of solving the word problem. We will discuss how questions concerning Dehn functions turn into questions concerning the geometry of certain planar 2-complexes called van Kampen diagrams. This translation also explains a link between Riemannian filling problems and word problems. Also, we will discuss the lower bounds on Dehn functions for semi-direct products of Z^n and Z. These results are classical and our approach is based on the work of Bridson and Gersten. | + | * **November 25**\\ <html> <span style="color:blue;font-size:120%"> (? University) </span></html> \\ **//Title//** \\ \\ <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP> |
| - | </WRAP> | + | |
| - | * **May 6**\\ <html> <span style="color:blue;font-size:120%"> No Algebra Seminar </span></html> \\ \\ <WRAP center box 90%> Have a good summer! Talks will resume in the fall. | + | * **December 2**\\ <html> <span style="color:blue;font-size:120%"> (? University) </span></html> \\ **//Title//** \\ \\ <WRAP center box 90%> **//Abstract//**: Text of Abstract </WRAP> |
| - | </WRAP> | + | |
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| * [[seminars:alge:alge-Spring2024|Spring 2024]] | * [[seminars:alge:alge-Spring2024|Spring 2024]] | ||
| * [[seminars:alge:alge-fall2024|Fall 2024]] | * [[seminars:alge:alge-fall2024|Fall 2024]] | ||
| + | * [[seminars:alge:alge-Spring2025|Spring 2025]] | ||
seminars/alge.1746046054.txt · Last modified: 2025/04/30 16:47 by daniel