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Colloquium

K. M. Rangaswamy, University of Colorado, Colorado Springs

Wednesday, April 3, at 4:10pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

Title: Are Leavitt path algebras really commutative algebras in non-commutative clothing?

Abstract:  Leavitt path algebras of directed graphs over a field are algebraic analogues of graph C*-algebras of operators on Hilbert spaces.  This talk is a report on some of the recent investigations illustrating two essential features of these algebras.  The first makes the Leavitt path algebras really useful tools in constructing examples of rings of various types.  The second is about the ideal lattice of Leavitt path algebras, which seems to posess similarities with commutative rings.  Various graphical constructions will illustrate these conclusions.

Colloquium

William Yslas Vélez, University of Arizona

Friday, April 5, at 4:10pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.

Increasing the mathematical content of the undergraduate curriculum for all students. Good for the student. Good for the university.

Abstract:  In the late 1980’s I began my efforts to increase the success rate of minorities in first semester calculus. These minority students came from all majors, though most were in engineering. The interventions that I devised were very time consuming and as the number of minority students increased, I could not manage that kind of effort. I developed my Calculus Minority Advising Program in an effort to meet with scores of minority students each semester. This program consists of a twenty-minute meeting with each student at the beginning of each semester. The meetings with the students eventually transformed my own attitude about the importance of mathematics in their undergraduate curriculum. It sloooowly dawned on me. The more mathematics a student took, the more opportunities were available to that student.

I took over the position of Associate Head for Undergraduate Affairs in the department in 2003. My work with minority students provided me with the tools to accept the new challenge of encouraging students to take more mathematics and to think about adding the math major or math minor to their program of study.

One can see the impact of these efforts across our university. With 600 mathematics majors and 700 mathematics minors, oftentimes the outstanding graduating senior in another department also has a mathematics major or minor. Our mathematics majors who also have another major are being accepted into graduate programs at the most elite universities in their other major.

The work that I do is focused on helping students reach their goals. Given the increasingly important role that mathematics now plays in society, taking more mathematics is essential. Mathematics departments need to communicate this to their students.

Doctoral Dissertation Defense

James Mixco, Saint Louis University

Thursday, April 11, 10:00am-12:00pm (the first hour is public), in Ritter 202

Supersymmetric Cluster Algebras and Their Quantum Deformations

Abstract:  Fomin and Zelevinsky introduced cluster algebras in 2001. A cluster algebra is a commutative ring generated by variables obtained by an iterative combinatorial process called mutation. From the time of their inception, cluster algebras have been found to have applications to several branches of mathematics and physics. These include algebraic geometry, Poisson geometry, Teichmuller space theory, combinatorics, and analysis.

More recently, an approach towards defining cluster algebras with Grassmann variables has been proposed by Ovsienko. This attempt has quite a few limitations. Here, we give an approach to supersymmetric cluster algebras independent of Ovsienko and provide some new interesting geometric examples. This work is largely based on the work done by Li, Mixco, Ransingh, and Srivastava. In addition to what is done by Li, Mixco, Ransingh, and Srivastava, we expand the theory of cluster superalgebras by proving theorems analogous to classical cluster algebra theorems. Beyond that, we extend our notion of cluster superalgebras to quantum cluster algebras.

Departmental Awards Ceremony

Friday, April 26 in Lee Lecture Hall. Refreshments at 4:00pm.  Ceremony begins at 4:20pm.

Featuring the 2019 Case Lecture:

How to win the lottery and get away with murder

by Dr. Liberty Vittert, Washington University in St. Louis

Spring 2019 Colloquium Schedule

Friday, February 15: Liberty Vittert, Washington University in Saint Louis

Friday, March 1: Tyler Bongers, Washington University in Saint Louis

Friday, March 22: Louis Kauffman, University of Illinois Chicago

Wednesday, April 3: K. M. Rangaswamy, University of Colorado, Colorado Springs

Friday, April 12: Mihai Ciucu, Indiana University