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--- seminars:alge:alge-fall2017 [2019/04/06 04:09] – tongviet
+++ seminars:alge:alge-fall2017 [2019/04/06 04:10] (current) – tongviet
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+~~META:title=Fall 2017~~
+<WRAP center box 68%>
+[[http://www-history.mcs.st-and.ac.uk/Biographies/Galois.html|{{http://www.win.tue.nl/~aeb/at/mathematicians/galois1.jpg?110*135 |Evariste Galois}}]]   [[ http://www-history.mcs.st-and.ac.uk/Mathematicians/Noether_Emmy.html|{{ http://seminars.math.binghamton.edu/AlgebraSem/emmy_noether.jpg?110*135|Emmy Noether}}]]
+\\  \\
+ <WRAP centeralign>
+**#####The Algebra Seminar#####**
+</WRAP></WRAP>
+Unless stated otherwise, the seminar meets Tuesdays in room WH-100E at 2:50 p.m. There will be refreshments served at 4:00 in room WH-102.
+Organizers: [[:people:alex:start|Alex Feingold]] and [[:people:mazur:start|Marcin Mazur]]
+To receive announcements of seminar talks by email, please join the seminar's [[http://www1.math.binghamton.edu/mailman/listinfo/algsem|mailing list]].
+----
+=====Fall 2017=====
+   * **August 29**\\ Organizational meeting
+   * **September 5**\\ <html> <span style="color:blue;font-size:120%">Dikran Karagueuzian </span></html>(Binghamton University) \\ **//Categories for the Skeptical Mathematician//** \\    \\  <WRAP center box 90%> **//Abstract//**: Many find it hard to see the mathematical content in Category Theory. I will discuss ways of understanding this content and how I recently decided that it is relevant to a problem in Commutative Algebra which I have studied.
+</WRAP>
+   * **September 12**\\ <html> <span style="color:blue;font-size:120%">Hung Tong-Viet </span></html> (Binghamton University)\\ **// Real class sizes  //** \\    \\  <WRAP center box 90%> **//Abstract//**:
+An element $x$ in a finite group $G$ is said to be **real** if there exists an element $g\in G$ such that $x^g=x^{-1}$. A real conjugacy class of $G$ is a conjugacy class  which contains some real element and   a real class size is the size of a real conjugacy class. Several arithmetic properties of the real class sizes can conveniently be stated using  graph theoretic language.
+The **prime graph** on the real  class sizes of a finite group $G$, denoted by $\Delta^*(G)$, is a simple graph with vertex set $\rho^*(G)$, the set of primes dividing some real class size of $G$, and there is an edge between two vertices $p$ and $q$ if the product $pq$ divides some real class size.
+In this talk, I will outline the proof that if  the prime graph on the real class sizes of a finite group is disconnected, then the group is solvable.
+</WRAP>
+   * **September 19**\\ <html> <span style="color:blue;font-size:120%">Phillip Wesolek </span></html> (Binghamton University) \\ **//Elementary amenability and bounded automata groups //** \\    \\  <WRAP center box 90%> **//Abstract//**: (Joint work with Kate Juschenko) The bounded automata groups are
+a natural family of groups, which are defined by a finite amount of
+information in the form of a certain type of finite automaton. A remarkable
+property of bounded automata groups is that they are necessarily amenable.
+On the other hand, the elementary amenable groups are groups that are
+amenable for `elementary reasons' and thus are somewhat uninteresting. One
+is thereby motivated to identify the non-elementary amenable bounded
+automata groups. We isolate three natural families of bounded automata
+groups, and in each family, we identify the elementary amenable groups.
+</WRAP>
+   * **September 26**\\ <html> <span style="color:blue;font-size:120%">Matt Evans </span></html> (Binghamton University)\\ **//Natural Dualities and BCK-algebras//** \\    \\  <WRAP center box 90%> **//Abstract//**: BCK-algebras are generalizations of Boolean algebras. There is a well-known natural duality between Boolean algebras and Stone spaces (totally disconnected, compact, Hausdorff spaces), and one might wish to develop a similar type of duality for the class of BCK-algebras. In this talk I will briefly review some category theory before defining "natural duality," and then discuss some progress on dualizing bounded commutative BCK-algebras.
+   * **This talk has been canceled due to illness of the speaker**.
+</WRAP>
+   * **October 3**\\ <html> <span style="color:blue;font-size:120%"> Joe Cyr </span></html> (Binghamton University)\\ **// Subdirectly Irreducible Medial Quandles of Set Type //** \\    \\  <WRAP center box 90%> **//Abstract//**: This talk will be a continuation of my seminar talk last semester on medial
+quandles (though no prior knowledge will be assumed). We will explore some
+important aspects of the structure of this class of algebras and find that
+the subdirectly irreducibles of set type are quasi-reductive. This then
+allows one to fully classify this class of subdirectly irreducible medial
+quandles.
+</WRAP>
+   * **October 10**\\ <html> <span style="color:blue;font-size:120%">Luise-Charlotte Kappe</span></html> \\ **//On covering numbers of groups//** \\    \\  <WRAP center box 90%> **//Abstract//**: A set of proper subgroups is a cover for a group if its union is the whole group. The minimal number of subgroups needed to cover a group is
+called its covering number. No group is the union of two proper subgroups. Tomkinson showed that the covering number of a solvable group has the form prime-power-plus-one and for each such integer there exists a solvable group
+having this integer as a covering number. In addition he showed that 7 is not a covering number. So far it has been shown that the integers < 27, which are not covering numbers, are 2,7,11,19,21,22 and 25. We extend this list by determining all integers < 129 which are covering numbers. This is joint work with Martino Garonzi and Eric Swartz.
+</WRAP>
+   * **October 17**\\ <html> <span style="color:blue;font-size:120%">Mark Skandera </span></html>(Lehigh) (joint with the Combinatorics Seminar, 1:15 - 2:15 PM, WH-100E) \\  **//  Evaluations of Hecke Algebra Traces at the Wiring Diagram Basis //** \\    \\  <WRAP center box 90%> **//Abstract//**:
+The (type A) Hecke algebra H<sub>n</sub>(q) is a certain module over **Z**[q<sup>1/2</sup>,q<sup>-1/2</sup>] which is a deformation of the group algebra of the symmetric group.  The **Z**[q<sup>1/2</sup>,q<sup>-1/2</sup>]-module of its trace functions has rank equal to the number of integer partitions of n, and has bases which are natural deformations of those of the trace module of the symmetric group algebra.  While no known closed formulas give the evaluation of these traces at the natural basis elements of H<sub>n</sub>(q), or at the Kazhdan-Lusztig basis, I present a combinatorial formula for the evaluation of traces induced by the sign character at a certain wiring diagram basis of H<sub>n</sub>(q).
+</WRAP>
+   * **October 24**\\ <html> <span style="color:blue;font-size:120%">Hung Tong-Viet
+</span></html> (Binghamton University)\\ **// 2-parts of real class sizes //** \\    \\  <WRAP center box 90%> **//Abstract//**: An element $x$ in a finite group G is said to be **real** if $x$ and  $x^{-1}$ are G-conjugate. A conjugacy class of G is said to be real if it contains real elements. A real class size is the size of a real conjugacy class. In this talk, I will discuss some results on the normal structures of groups with restrictions on the 2-parts of the real class sizes.
+</WRAP>
+   * **October 31**\\ <html> <span style="color:blue;font-size:120%">Eran Crockett </span></html> (Binghamton University)\\ **// The dualizability problem for nilpotent algebras  //** \\    \\  <WRAP center box 90%> **//Abstract//**: A finite algebra is dualizable if there is a certain dual
+representation of a category of algebras in a category of topological
+relational structures. After giving a careful definition of this concept,
+we ask which finite algebras are dualizable. In particular, I exhibit a
+class of dualizable nilpotent algebras and ask whether algebras in a
+generalization of this class are also dualizable.
+</WRAP>
+   * **November 7**\\ <html> <span style="color:blue;font-size:120%">Hung Nguyen</span></html> (The University of Akron) \\ **// On the average of character degrees   //** \\    \\  <WRAP center box 90%> **//Abstract//**: We use the notion of average character degrees to improve some classical
+results in the character theory of finite groups such as the Ito-Michler theorem,
+Thompson’s theorem and Navarro-Tiep’s theorem.
+</WRAP>
+   * **November 14**\\ <html> <span style="color:blue;font-size:120%">Victor Protsak </span></html> (Cornell University)\\ **//Representations of $\mathfrak{gl}(n)$: a theme and variations//** \\    \\  <WRAP center box 90%> **//Abstract//**: Finite-dimensional representation theory of $\mathfrak{gl}(n)$,
+the general linear Lie algebra of $n\times n$ matrices, has three well-known aspects: algebraic (highest weight theory and characters), algebro-geometric (flag varieties and standard monomials) and combinatorial (Gelfand-Tsetlin theory and Young tableaux). Perhaps less familiar is the noncommutative linear algebra aspect, rooted in the universal enveloping algebra and involving Capelli determinants and characteristic identities.
+We will review these aspects of representation theory of $\mathfrak{gl}(n)$ and explore generalizations in two different directions: infinite-dimensional modules over $\mathfrak{gl}(n)$ and integrable modules over the infinite general linear Lie algebra $\mathfrak{gl}(\infty)$.
+</WRAP>
+   * **November 21**\\ <html> <span style="color:blue;font-size:120%">Ian Payne </span></html> (McMaster University)\\ **//
+  Subdirectly Irreducible Algebras: Big and Small  //** \\    \\  <WRAP center box 90%> **//Abstract//**: Given a finite algebra, there is a class called its "generated
+variety". For example, it can be shown that the variety generated by the
+two-element group is precisely the class of groups of exponent two. In any
+generated variety, there is a subclass of "subdirectly irreducible"
+members. This subclass depends only on the generating algebra, and
+universal algebraists are interested in knowing how large the subclass is
+for a given algebra. This main goals of this talk are to say what
+subdirectly irreducible algebras are, explain why they are of interest,
+and discuss some known results about the number of subdirectly irreducible
+members in some generated varieties.
+</WRAP>
+   * **November 28**\\ <html> <span style="color:blue;font-size:120%"> Upstate Descriptive Set Theory and
+Group Theory Day
+</span></html> \\ **//Several Talks 1:00 - 6:00//** \\    \\  <WRAP center box 90%> **//Abstract//**:
+Please follow this link for details about the special talks: [[http://people.math.binghamton.edu/wesolek/northeast/meeting.html|Website for this meeting]]
+</WRAP>
+   * **December 5 **\\ <html> <span style="color:blue;font-size:120%">Matt Evans </span></html> (Binghamton University)\\ **//Natural Dualities and BCK-algebras//** \\    \\  <WRAP center box 90%> **//Abstract//**: BCK-algebras are generalizations of Boolean algebras. There is a well-known natural duality between Boolean algebras and Stone spaces (totally disconnected, compact, Hausdorff spaces), and one might wish to develop a similar type of duality for the class of BCK-algebras. In this talk I will briefly review some category theory before defining "natural duality," and then discuss some progress on dualizing bounded commutative BCK-algebras.
+</WRAP>
+----
+----
+  * [[http://seminars.math.binghamton.edu/AlgebraSem/index.html|Pre-2014 semesters]]\\
+  * [[seminars:alge:fall2014]]
+  * [[seminars:alge:spring2015]]
+  * [[seminars:alge:alge_fall2015]]
+  * [[seminars:alge:alge-spring2016]]
+  * [[seminars:alge:alge-fall2016]]
+  * [[seminars:alge:alge-Spring2017|Spring 2017]]
+<html>
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+</html>