Algebra Seminar/Colloquium Schedule 

Organizers: Ela Celikbas (ela.celikbas [at] math.wvu.edu) and Olgur Celikbas (olgur.celikbas [at] math.wvu.edu)

 Algebra Seminar/Colloquium Schedule for Fall 2018         

  • Michelle Homp, University of Nebraska - Lincoln     
    • Friday, November 30, 2018,  ARM 315, 3:30pm-4:30pm    
    • Title: Master of Arts for Teachers: A Mathematics Degree Designed with Teachers in Mind
    • Abstract:  It is widely recognized that effective mathematics teaching requires highly specialized content knowledge. Whether preparing future teachers or providing professional development for veteran teachers, the CBMS publication, The Mathematical Education of Teachers II, recommends that content in advance mathematics courses ``should be tailored to the work of teaching, examining connections between middle grades and high school mathematics as well as those between high school and college." In this presentation we discuss the development of the Master of Arts for Teachers (MAT) degree program at the University of Nebraska -- Lincoln (UNL), its curriculum development, strategies used to ensure strong connections to the classroom, teacher-friendly delivery strategies (both in-person and online), and how the MAT became one of the largest summer graduate programs at UNL.
    • Click here for the flyer of the talk. 
  • David Jorgensen, University of Texas at Arlington 
    • Thursday, November 29, 2018,  ARM 315, 4pm-5pm    
    • Title: Beyond matrix factorizations
    • Abstract:  Matrix factorizations of polynomial functions were introduced and studied by David Eisenbud in 1980.  In the 1990's, Maxim Kontsevich proposed that matrix factorizations provide a good mathematical model of certain objects in string theory.  We give a basic overview of matrix factorizations, discuss their major applications, and present some recent further directions.
    • Click here for the flyer of the talk.
  • Jugal Verma - IIT Bombay, India 
    • Thursday, September 20, 2018,  ARM 315, 4pm-5pm    
    • Title: Milnor numbers of hypersurface singularities, mixed multiplicities of  ideals and volumes of polytopes
    • Abstract:  If $H$ is an analytic surface defined by $f=0$  in $\mathbb C^{n+1}$ with an isolated singularity at the origin, then the colength of the Jacobian ideal $J(f)$ is called its Milnor number. B. Teissier refined this notion by a sequence of $\mu^*(H)$ Milnor numbers of intersections of $H$ with general linear spaces of dimension $i$ for $i=0,1,\dots, (n+1).$ J. J. Risler and Teissier showed that this sequence coincides with the mixed multiplicities of the maximal ideal and $J(f).$ They proposed conjectures about log-convexity of the $\mu^*(H)$ which were solved by B. Teissier, D. Rees-R. Y. Sharp and D. Katz. These give rise to Minkowski inequality and equality for the Hilbert-Samuel multiplicities of ideals. Mixed multiplicities are also connected with volumes of polytopes and hence to counting solutions to polynomial equations. 
    • Click here for the flyer of the talk.
  • Yongwei, Yao - Georgia State University
    • Friday, August 17, 2018, ARM 315, 4pm-5pm    
    • Title: Lech's inequality, the Stuckrad-Vogel conjecture, and uniform behavior of Koszul homology
    • Abstract:  Let $(R, \mathfrak{m})$ be a Noetherian local ring, and let $M$ be a finitely generated $R$-module of dimension $d$. We prove that the set $\displaystyle{\left\{\frac{l(M/IM)}{e(I, M)} \right\}_{\sqrt{I}=\mathfrak{m}}}$ is bounded below by ${1}/{d!e(\overline{R})}$, where $\overline{R}=R/\operatorname{Ann}(M)$. Moreover, when $\widehat{M}$ is equidimensional, this set is bounded above by a finite constant depending only on $M$. The lower bound extends a classical inequality of Lech, and the upper bound answers a question of St\"{u}ckrad-Vogel in the affirmative. As an application, we obtain results on uniform behavior of the lengths of Koszul homology modules. This is joint work with Patricia Klein, Linquan Ma, Pham Hung Quy, and Ilya Smirnov.
    • Click here for the flyer of the talk.
  •   Tokuji Araya - Okayama University of Science, Japan 
    • Thursday, August 16, 2018, ARM 315, 4pm-5pm    
    • Title: An introduction to Path Algebras
    • Abstract:  Let $k$ be a field and let $Q$ be a quiver (i.e., $Q$ is a directed graph where loops and multiple arrows between two vertices are allowed, namely a multidigraph). The path algebra $kQ$ of $Q$ is a $k$-algebra whose basis is the set of paths in $Q$. Since any finite dimensional $k$-algebra is Morita equivalent to a factor algebra of some path algebra, it is very significant to investigate path algebras. In this talk, we will recall the definition and some properties of path algebras. This talk will be accessible to graduate students. 
    • Click here for the flyer of the talk.         

  Past Algebra Seminar/Colloquium Talks