**Seminars and Colloquiums**

for the week of February 8, 2016

for the week of February 8, 2016

*SPEAKER:*

Mark Bly, UTK, Monday

Kei Kobayashi, UTK, Tuesday

Kelly Rooker, UTK, Thursday

Jerome Goddard II, Auburn University Montgomery, Thursday

Sergei Tabachnikov, Penn State University, Thursday

Stefan Richter, UTK, Friday

Sergei Tabachnikov, Penn State, Friday

*TEA TIME
3:00 – 3:30 pm, Ayres 401
Monday, Tuesday, & Wednesday
Hosted by Ibrahim & Alan, UTK *

**Monday, February 8th**

TOPOLOGY AND GEOMETRY SEMINAR

TITLE: Intro to Algebraic Geometry, Part II

SPEAKER: Mark Bly, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres 113

We'll firm up a few points that were a bit rushed in the whirlwind nature of last week's talk. Then, we'll show how projective space is a natural extension of affine space, observing some of its nicer properties. We'll also show how the notion of the Zariski topology can be extended from varieties in affine space to rings in general.

** Tuesday, February 9th **

STOCHASTICS SEMINAR

TITLE: Small ball probabilities for a class of time-changed self-similar processes

SPEAKER: Kei Kobayashi, UTK

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

A standard Brownian motion composed with the so-called "inverse stable subordinator" is used to model subdiffusion, where particles spread more slowly than the classical Brownian particles. This new stochastic process is significantly different from the Brownian motion; indeed, it is neither Markovian nor Gaussian and has transition probabilities satisfying a fractional-order heat equation.

Now, consider the probability that the process does not exit a small ball during the unit time interval. As the radius of the ball approaches zero, the probability converges to zero, but what is the rate of convergence? A special case of our results (originally proved by Nane in 2009) states that the probability decays polynomially. This is interesting since, for the Brownian motion, the corresponding probability decays exponentially. We extended this result to a large class of self-similar processes composed with general inverse subordinators.

** Thursday, February 11th **

MATH ECOLOGY/ EVOLUTION SEMINAR

SPEAKER: Kelly Rooker, UTK

TIME: 10:00am – 11:00am

ROOM: Ayres 404

Chapter 4 of Bowles & Gintis book “Cooperative Species”

DIFFERENTIAL EQUATIONS SEMINAR: COSPONSORED BY THE SIAM STUDENT CHAPTER

TITLE: Modeling the effects of habitat fragmentation via reaction diffusion equations

SPEAKER: Jerome Goddard II, Auburn University Montgomery

TIME: 2:10pm - 3:25pm

ROOM: Ayres 405

Two important aspects of habitat fragmentation are the size of fragmented patches of preferred habitat and the inferior habitat surrounding the patches, called the matrix. Ecological field studies have indicated that an organism’s survival in a patch is often linked to both the size of the patch and the quality of its surrounding matrix. In this talk, we will focus on modeling the effects of habitat fragmentation via the reaction diffusion framework. First, we will introduce the reaction diffusion framework and a specific reaction diffusion model with logistic growth and Robin boundary condition (which will model the negative effects of the patch matrix). Second, we will explore the dynamics of the model via some methods from nonlinear analysis and ultimately obtain a causal relationship between the size of the patch and the quality of the matrix versus the maximum population density sustainable by that patch

JUNIOR COLLOQUIUM

TITLE: Proofs (not) from the Book

SPEAKER: Sergei Tabachnikov, Penn State University

TIME: 3:40pm - 4:35pm

ROOM: Ayres 405

The eminent mathematician of the 20th century, Paul Erdos, often mention "The Book" in which God keeps the most elegant proof of every mathematical theorem. So, attending a mathematical talk, he would say: "This is a proof from The Book", or "This is a correct proof, but not from The Book". M. Aigner and G. Ziegler authored the highly successful "Proofs from THE BOOK" (translated into 13 languages). In this talk, I shall present several proofs that are not included in the Aigner-Ziegler book but that, in my opinion, could belong to "The Book".

** Friday, February 12th **

ANALYSIS SEMINAR

TITLE: Functions as quotients of multipliers, III

SPEAKER: Stefan Richter, UTK

TIME: 2:30pm - 3:20pm

ROOM: Ayres 121

COLLOQUIUM

TITLE: Pentagram Map, twenty five years after

SPEAKER: Sergei Tabachnikov, Penn State

TIME: 3:30pm-4:30pm

ROOM: Ayres 405

Introduced by R. Schwartz about 25 years ago, the pentagram map acts on plane n-gons, considered up to projective equivalence, by drawing the diagonals that connect second-nearest vertices and taking the new n-gon formed by their intersections. The pentagram map is a discrete completely integrable system whose continuous limit is the Boussinesq equation, a completely integrable PDE of soliton type. In this talk I shall survey recent work on the pentagram map and its generalizations, emphasizing its close ties with the theory of cluster algebras, a rapidly developing area with numerous connections to diverse fields of mathematics. In particular, I shall describe a higher-dimensional version of the pentagram map and, somewhat counter-intuitively, its 1-dimensional version.

*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 colloquium AT math DOT utk DOT edu *

**Past notices:**