# Colloquia

## Hung Tran

Some selection problems in the theory of viscosity solutions

Abstract: I will explain some interesting selection problems in nonlinear PDEs. The basic question is about how to select one good solution out of many reasonable ones. A question of this type led to the whole theory of viscosity solutions in 1980s. Then I will focus on the vanishing discount problem and describe the main results, which solve an open question also in 1980s. This is a joint work with Ishii and Mitake.

Date: 4/28/2017

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

All are welcome.

## David Offner

Polychromatic Colorings on Hypercubes, Complete Graphs, and Integers

Abstract: Given a set S, and a set T of subsets of S, a coloring of the elements of S is called T -polychromatic if every set in T contains an element of every color. Let polyT (S) be the largest n for which there is a T -polychromatic coloring of S with n colors. This talk introduces theorems and open problems on the value of polyT (S) in three settings:

• S is the set of edges of a hypercube, and T is the set of all subgraphs isomorphic to

a given graph H.

• S is the set of edges of a complete graph, and T is the set of all regular spanning

subgraphs of a given degree.

• S is the set of integers, and T is the set of translates of a given finite set.

Date: 4/26/2017

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

All are welcome.

## Juan Pablo Mejia-Ramos

Developing valid and reliable measures to assess students' comprehension of the proofs that they read

Abstract: In this talk I will focus on the assessment of undergraduate students' reading comprehension of mathematical proofs, discussing a research program aimed at developing and validating reliable proof comprehension tests. I will present findings on students performance on three of these tests and discuss what we can learn from using this kind of measures in the mathematics classroom and in mathematics education research.

Date: 4/21/2017

Time: 2:30PM-3:30PM

Place: 315 Armstrong Hall

All are welcome.

## Deborah Chun

Matroids and wilder things: Polymatroids and Delta-matroids

Abstract: Matroids will be introduced in this talk. I will give an example of a result for general matroids, which has interesting corollaries in more specialized classes of structures, like graphs. I will also discuss two generalizations of matroids. In polymatroids, I will give a conjecture from Vertigan, that, if true, has an important corollary in matroid theory. That is, it gives us Rota's conjecture. In delta-matroids, I will present a splitter theorem.

Date: 4/13/2017

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

All are welcome.

## Hiroki Matsui

Thick subcategories of modules and characterizations of local rings

Abstract: View

Date: 4/12/2017

Time: 4:00PM-5:00PM

Place: 313 Armstrong Hall

All are welcome.

## C.F. Jeff Wu

From real world problems to esoteric research: examples and personal experience

Abstract: Young (and some not-so-young) researchers often wonder how to extract good research ideas and develop useful methodologies from solving real world problems. The path is rarely straightforward and its success depends on the circumstances, tenacity and luck. I will use three examples to illustrate how I trod the path. The first involved an attempt to find optimal growth conditions for nano structures. It led to the development of a new method “sequential minimum energy design (smed)”, which exploits an analogy to potential energy of charged particles. After a few years of frustrated efforts and relentless pursuit, we realized that smed is more suitable for generating samples adaptively to mimic an arbitrary distribution rather than for optimization. The main objective of the second example was to build an efficient statistical emulator based on finite element simulation results with two mesh densities in cast foundry operations. It eventually led to the development of a class of nonstationary Gaussian process models that can be used to connect simulation data of different precisions and speeds. The third example is about sequential design that works well for small samples in sensitivity testing. I will describe three major papers in a span of 30 years and how each paper had one new idea that inspired the next paper. In each example, the developed methodology has broader applications beyond the original problem. I will explain the thought process in each example. Finally, I will share some secrets about a “path to innovation”.This talk will have many illustrative examples, and should be accessible to graduate students.

Date: 4/06/2017

Time: 3:30PM-4:30PM

Place: Evansdale Crossing 414

All are welcome.

## Hiroki Matsui

Thick subcategories of modules and characterizations of local rings

Abstract: View

Date: 4/05/2017

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

All are welcome.

## Ananthnarayan Hariharan

Idealizations and Connected sums

Abstract: We will begin with an introduction to Gorenstein rings using partial derivatives.

Two special constructions are idealizations and connected sums.

The goal of this talk is to understand the connection between them.

This talk will have many illustrative examples, and should be accessible to graduate students.

Date: 3/28/2017

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

All are welcome.

## RUME Seminar

Improving Student Understanding of Multivariable Calculus Concepts with CalcPlot3D

Dr. Monica VanDieren from Robert Morris will present.

Abstract: CalcPlot3D is a free, online applet which provides students opportunities to dynamically visualize and experiment with 3D transformations, rotations, and computations of multivariable calculus concepts. VanDieren is PI on a collaborative NSF Grant No. 1523786 which aims to (1) develop and test a series of new visual concept explorations and applications in CalcPlot3D; (2) expand the features of CalcPlot3D to accommodate the new concept explorations and address applications in differential equations, linear algebra, physics, and engineering; and (3) develop and test an assessment tool to measure student understanding of multivariable calculus concepts. In this presentation, she will cover some of the features of CalcPlot3D and report on preliminary research on student understanding of the cross product.

Date: 3/28/2017

Time: 11:30AM-12:30PM

Place: 315 Armstrong Hall

All are welcome.

## Jerzy Weyman

From quiver representations to cluster algebras

Weyman got his Ph.D. in Mathematics from Brandeis University in 1980. His interests include several branches of algebra: Commutative Algebra, Algebraic Geometry, Representation Theory and Invariant Theory. After working for five years at the Institute of Mathematics of the Polish Academy of Sciences, he joined the faculty of Northeastern University in Boston. Since 2013, he is Joan and Stuart Sydney Professor of Mathematics at the University of Connecticut. Professor Weyman was the recipient of the Kuratowski Prize of the Polish Mathematical Society in 1983. He was awarded the Humboldt Research Prize in 2011. He was the recipient of the 2015 Wacław Sierpiński Medal of the Polish Mathematical Society which is given out annually to recognize Polish mathematicians for their outstanding work and scientific achievements in their fields.

Abstract: Pdf

Date: 3/16/2017

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

All are welcome.

## Pages