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--- seminars:alge:alge_fall2015 [2016/01/26 19:38] – created alex
+++ seminars:alge:alge_fall2015 [2018/01/11 00:34] (current) – mazur
@@ Line 1: / Line 1: @@
+~~META:title=Fall 2015~~
+   * **September 1**\\  Organizational Meeting
+   * **September 8**\\  <html> <span style="color:blue;font-size:120%">Tuval Foguel</span></html> (Adelphi University)\\      **//Partition Numbers of Finite Groups//** \\    \\  <WRAP center box 90%> **//Abstract//**: A group partition is a group cover in which the elements have trivial pairwise intersection. Here we define the partition number of a group - the minimal number of subgroups necessary to form a partition - and examine some of
+its properties, including its relation to the covering number.
+</WRAP>
+   * **September 15**\\  <html> <span style="color:blue;font-size:120%">No Meeting</span></html> \\ **// //** \\    \\  <WRAP center box 90%> **//Abstract//**: None
+</WRAP>
+   * **September 22**\\  <html> <span style="color:blue;font-size:120%">No Meeting</span></html> \\ **// //** \\    \\  <WRAP center box 90%> **//Abstract//**: None
+</WRAP>
+   * **September 29**\\  <html> <span style="color:blue;font-size:120%">Mathew Wolak</span></html> (Binghamton University)\\      **//The centers of universal enveloping algebras of contracted Lie groups//** \\    \\  <WRAP center box 90%> **//Abstract//**: Lie group contraction is a process which ``flattens out'' a Lie group. We explore how the center of the universal enveloping algebra of a contracted Lie group relates to that of the original group. We will look in particular at the Galilean group and a contraction of SU(n).
+</WRAP>
+   * **October 6**\\  <html> <span style="color:blue;font-size:120%">Ben Brewster</span></html> (Binghamton University)\\      **//The Chermak-Delgado Lattice//** \\    \\  <WRAP center box 90%> **//Abstract//**: The Chermak-Delgado is the lattice introduced by Chermak and Delgado [3] and presented in a more limited form by Isaacs [5]. In a finite group, there are finite lattices – the subgroup lattice, the lattice of subnormal subgroups and the subgroups which have maximal measure in the limited measure present by Isaacs. These are listed in a nested order here.
+Recently there has been interest in the nature of these lattices. I will review some of the properties of the Chermak-Delgado lattice. Then as time allows, I will describe some of these developments as presented in [1,2,4,6].
+References:
+.  Brewster, Hauck and Wilcox, Groups whose Chermak-Delgado lattice is a chain.  J. Group Theory 17 (2014) 253-279.
+. Brewster, Hauck and Wilcox, Quasi-Antichain Chermak-Delgado Lattices of finite groups.  Arch. Math.
+.  Chermak and Delgado, A measuring argument for finite groups.  Proc. AMS 107 (1989) 907-914.
+.  Cocke, Subnormality and the Chermak-Delgado Lattice, (private communication)
+.  Isaacs, Finite Group Theory.  A.M.S. 2008
+.  McCulloch, Chermak-Delgado simple groups.  (private communication)
+</WRAP>
+   * **October 13**\\  <html> <span style="color:blue;font-size:120%">Robert Bieri</span></html> (Binghamton University)\\      **// Groups of piecewise isometric permutations of lattice points       //** \\    \\  <WRAP center box 90%> **//Abstract//**:
+An orthant (of the orthogonal integral lattice) $L\subseteq \mathbb Z^n$ is the image of the standard orthant $\mathbb ℕ^n$
+under an affine-orthogonal transformation. And a permutation $p: S\longrightarrow S$ of a subset $S\subseteq \mathbb Z^n$ is
+piecewise-Euclidean-isometric (pei), if $S$ is a disjoint union of finitely many orthants, $S = \bigcup_{i}L_i$, on
+each of which $p$ restricts to an isometric embedding $L_i\rightarrow S$. I will talk about the group
+$\text{pei}(S)$ of all
+pei-permutations of various subsets $S$ and its subgroup $\text{pet}(S)$ of all piecewise-Eucliden-translation
+permutations. In the case when $S$ consists of the lattice points on the union of $n$ positive coordinate
+axes then $\text{pet}(S)$ is the Houghton group $H_n$.
+This is joint work with Heike Sach: we prove finiteness properties of some pei- and pet- groups,
+and have, as a consequence, that $\text{pei}(\mathbb Z^n)$ admits a K(G,1)-complex with finite $(2^n – 1)$-skeleton.
+An interesting point is that prominent groups like Richard Thompson's group $V$ crop up when we
+extend the consideration to the $\text{SL}_2(\mathbb Z)$-lattice in the hyperbolic plane. .
+</WRAP>
+   * **October 20**\\  <html> <span style="color:blue;font-size:120%">Adam Allan</span></html> (Binghamton University)\\      **// Algorithmic Detection of Self-Injectivity //** \\    \\  <WRAP center box 90%> **//Abstract//**:  In this talk I will briefly review what it means for a finite
+dimensional associative algebra over a field k to be self-injective and
+then I will present newly discovered results for the computational
+verification of when an algebra is self-injective. These are of interest
+both for computer algebra and for establishing bounds on certain invariants
+for an algebra. Some examples of these methods applied to centralizer
+algebras will also be included.
+</WRAP>
+   * **October 27**\\  <html> <span style="color:blue;font-size:120%"> David Biddle  </span></html> (Binghamton University)\\      **//On The Probability of Generating a Finite Nilpotent Group//** \\    \\  <WRAP center box 90%> **//Abstract//**: One can define the probability of generating a f.g. group $G$ by $k$ (random uniform) elements by defining $P_k(G)=|S_k(G)|/|G|^k$ where $S_k(G)$ is the set of ordered generating $k$-tuples of $G$. First we demonstrate for all groups of size $|G|\leq 2^m$ we have $P_k(G)\geq P_k(\mathbf{Z/2}^m)$. We then give bounds on $P_k(G)$ based on simply the minimum number of generators of $G$ (or 'rank of $G$) if $G$ is finite
+nilpotent. We combine these to show that for any finite group $G$ and $1>\epsilon >0$, for $k>\log_2(|G|/\epsilon )+2$, we have $P_k(G)>1-\epsilon$.
+</WRAP>
+   * **November 3**\\  <html> <span style="color:blue;font-size:120%">Eran Crockett</span></html> (Binghamton University)\\      **// Dualizability in Congruence Distributive Varieties  (first part of the admission to candidacy exam) //** \\    \\  <WRAP center box 90%> **//Abstract//**: We show that a finite algebra that generates a congruence
+distributive variety is dualizable if and only if it has a near unanimity
+term operation.
+</WRAP>
+   * **November 10**\\  <html> <span style="color:blue;font-size:120%">Joseph Cyr</span></html> (Binghamton University)\\      **//Some Mal'cev Conditions on Congruence n-Permutable Varieties//** \\    \\  <WRAP center box 90%> **//Abstract//**: A (strong) Mal'cev condition provides an equivalence between some property of a variety and the existence of certain terms satisfying given identities. I will introduce the theorem due to Mal'cev for which this topic gets its name and then prove a generalized version of that theorem. I will also show how this relates to groups and other algebras.
+</WRAP>
+   * **November 17**\\  <html> <span style="color:blue;font-size:120%">Daniel Franz </span></html> (University of Virginia)\\      **// Quantifying the Residual Finiteness of Linear Groups  //** \\    \\  <WRAP center box 90%> **//Abstract//**:  In a similar vein as subgroup growth, one can study the residual finiteness
+growth of a residually finite group, which measures how well a group is
+approximated by its finite quotients. I will introduce this recently
+developed invariant and give examples for certain groups. I will then focus
+on linear groups, for which the normal and non-normal residual finiteness
+growth functions are polynomial. Specifically, I will compute the exact
+asymptotics for these growth functions for Chevalley groups over rings of
+integers in both characteristic 0 and p, which are polynomial of degree the
+dimension of the group and the codimension of a maximal parabolic subgroup,
+respectively.
+</WRAP>
+   * **November 24**\\  <html> <span style="color:blue;font-size:120%">Matt Evans</span></html> (Binghamton University)\\      **//A Dual Equivalence for Distributive Nearlattices//** \\    \\  <WRAP center box 90%> **//Abstract//**: In 1936, M.H. Stone showed that there is a duality between the category of Boolean algebras and the category of Stone spaces. This talk will present a result of Celani and Calomino (2014) demonstrating a dual equivalence between distributive nearlattices and N-spaces which extends the well-known Stone duality.
+</WRAP>
+   * **December 1**\\  <html> <span style="color:blue;font-size:120%">  </span></html> (Binghamton University)\\      **//A long title of the talk//** \\    \\  <WRAP center box 90%> **//Abstract//**: content of the abstract.
+</WRAP>
+   * **December 8**\\  <html> <span style="color:blue;font-size:120%">Joseph Mennuti</span></html> (Binghamton University)\\      **//  An Alternative Proof of Lagrange's Four-Square Theorem //** \\    \\  <WRAP center box 90%> **//Abstract//**: The classical proof of Lagrange's Four-Square Theorem is a
+modular arithmetic type argument, but this will be a proof that involves
+the quaternions.
+</WRAP>
+   * **December 15**\\  <html> <span style="color:blue;font-size:120%"> John Brown</span></html> (University)\\      **//An Introduction to Milnor K-Theory//** \\    \\  <WRAP center box 90%> **//Abstract//**: We will define the Milnor K-Theory of a field, have some quick examples, and finish with a discussion of the transfer/norm map.
+</WRAP>