**Seminars and Colloquiums**

for the week of September 23, 2019

for the week of September 23, 2019

*SPEAKERS*

**Monday**

Louis Gross, UTK
**
Tuesday
**Maximilian Pechmann, UTK

**Wednesday**

Lauren Ruth, Vanderbilt University

Slimane Adjerid, Virginia Tech

**Thursday**

Mat Langford, UTK

David Talmy, UTK

**Friday**

Mary Pilgrim, San Diego State University

**Tea Time -Canceled for this week
**

**Monday, September 23**

**MATH BIOLOGY SEMINAR
**TITLE: Mathematical Theories of Everything: Introduction to Catastrophe Theory

SPEAKER: Louis Gross, UTK

TIME: 10:10 am

ROOM: Claxton 105

Abstract:

**Tuesday, September 24**

**PROBABILITY AND STOCHASTICS SEMINAR
**TITLE: Bose-Einstein condensation in random potentials – Pt. 2

SPEAKER: Maximilian Pechmann, UTK

TIME: 2:10 PM

ROOM: Ayres 112

Abstract: It is known that random potentials can enhance the occurrence of some type of condensate in Bose gases. With the exception of a few special cases, it is, however, unclear whether such a condensation is actually a Bose-Einstein condensation (BEC). After introducing the definition of BEC, we discuss the results that are known so far concerning the occurrence of BEC in noninteracting Bose gases that are placed in random potentials. We introduce the Luttinger-Sy model (LSM), which is a central model in this research area and one of the very few random models for which the occurrence of BEC has been rigorously proved. Very recently, the occurrence of BEC has also been shown for a generalization of the LSM, and we discuss the main idea of the proof. Lastly, we give an overview of the case where the particles of the Bose gas interact with each other.

**Wednesday, September 25**

**ANALYSIS SEMINAR
**TITLE: Von Neumann Equivalence and Properly Proximal Groups

SPEAKER: Lauren Ruth, Vanderbilt University

TIME: 2:30 PM

ROOM: Ayres 113

Abstract: We introduce a new equivalence relation on groups, which we call von Neumann equivalence, and which is coarser than both measure equivalence and W*-equivalence. We introduce a general procedure for inducing actions in this setting and use this to show that many analytic properties, such as amenability, property (T), and the Haagerup property, are preserved under von Neumann equivalence. We also show that proper proximality, which was defined recently by Boutonnet, Ioana, and Peterson using dynamics, is preserved under von Neumann equivalence. In particular, proper proximality is preserved under both measure equivalence and W*-equivalence, and from this we obtain examples of non-inner amenable groups which are not properly proximal. This is joint work with Ishan Ishan and Jesse Peterson.

**COMPUTATIONAL & APPLIED MATH SEMINAR
**TITLE: High Order Immersed Finite Element Methods for Interface Problems

SPEAKER: Slimane Adjerid, Virginia Tech

TIME: 3:35 PM

ROOM: Ayres 112

Abstract: Many physical phenomena such as heat conduction and wave propagation in inhomogeneous media is modeled by partial differential equations with discontinuous coefficients referred to as interface problems. We introduce and motivate the immersed finite element approach for solving interface problems. The immersed finite element methods allow elements to be cut by the interface leading to special piecewise polynomial finite element spaces and modified weak formulations.

A brief historical review of immersed finite element methods will be presented. We will show how to construct high order immersed finite element spaces and weak Galerkin formulations for high accuracy computations. We discuss few properties of immersed finite element spaces and present computational results for several applications from acoustics and fluid dynamics and conclude with a list of open questions and future research projects.

**Thursday, September 26**

**DIFFERENTIAL EQUATIONS SEMINAR**

TITLE: Concavity of the arrival time I

SPEAKER: Mat Langford, UTK

TIME: 2:10 PM-3:25 PM

ROOM: Ayres 112

Abstract: A natural question that arises in the study of elliptic and parabolic PDE asks “when is the solution to a given problem a concave function?”. A related question concerns the convexity of the level sets of a solution. Of course, whereas a function is concave only if its level sets are convex, the converse is certainly not true. In this talk, I will present a beautiful argument, discovered in the '80s by N. Korevaar, which demonstrates the concavity of solutions to a very large class of problems, and discuss some important applications. In my following talk (based on joint work with Theodora Bourni), I will focus on certain curvature flow equations; I will show how Korevaar’s argument can be modified to obtain a sharp power-concavity property of the time-of-arrival function, and explain why this is interesting.

**MATH DATA SCIENCE SEMINAR
**TITLE: Parameterizing diverse microbial communities within ocean biogeochemical models

SPEAKER: David Talmy, UTK

TIME: 2:10 PM-3:10 PM

ROOM: Ayres 111

Abstract: Ocean microbial ecosystems are responsible for approximately half of all global primary productivity. Understanding global scale impacts of diverse microbes requires representation of microscale phenomena in ocean circulation and Earth system models. Here I develop idealized representations of contrasting microbial lifestyles and embed them within large-scale ocean models. I discuss challenges of accounting for diversity of microbial ecosystems within ocean models, and consider possible ways to simplify complexity while still accounting robustly for mechanisms that drive ecosystem function.

**Friday, September 27**

**COLLOQUIUM**

TITLE: Supporting Students through Calculus I: The Story of a Stretched Calculus Course

SPEAKER: Mary Pilgrim, San Diego State University

TIME: 3:35 PM

ROOM: Ayres 405

Abstract: Although there has been a national call to increase the number of STEM graduates in the United States, high failure rates in mathematics courses such as Calculus I continue acting as gatekeepers (PCAST, 2012). While the reasons contributing to high failure rates are complex, the traditional Calculus I course model does not necessarily “provide the desired level of support” for students to be successful (Voigt et al., 2017, p. 32). Experiences in Calculus I play an important role in the retention of STEM majors (Bressoud & Rasmussen, 2015; Ellis, Fosdick, & Rasmussen, 2016; Seymour & Hewitt, 1997), and institutions often find that their students, while placing into Calculus I, lack the necessary prerequisite knowledge to be successful in Calculus I (e.g. Agustin & Agustin, 2009; Sonnert & Sadler, 2014).

In this interactive talk, I will share an example of a successful stretched Calculus I model implemented to support students who self-identified as being unprepared for Calculus I. The stretched course (1) utilized evidence-based practices (as supported by Freeman et al., 2014), (2) addressed prerequisite knowledge, and (3) supported the development of study habits and metacognitive strategies (e.g. Ohtani & Hisasaka, 2018; Schneider & Artelt, 2010). Students who completed the stretched course outperformed their “regular” Calculus I student counterparts, were successful in subsequent mathematics courses and Engineering programs, and spoke of the continued impacts the course had a year after completion.

*If you are interested in giving or arranging a talk
for one of our seminars or colloquiums, please review our
calendar. *

*If you have questions, or a date you would like to confirm,
please contact Dr. Christopher Strickland, cstric12@utk.edu *

**Past notices:**