**Seminars and Colloquiums**

for the week of October 3, 2016

for the week of October 3, 2016

*SPEAKER:*

Arkady Leiderman, Ben-Gurion University of the Negev, Beer Sheva, Israel, Monday

Cara Sulyok, UTK, Monday

Chase Worley, UTK, Wednesday

Cory Hauck, ORNL/UTK, Wednesday - cancelled

*TEA TIME -
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401*

*Hosted by: Hannah Thompson*

**Monday, October 3rd **

TOPOLOGY/GEOMETRY SEMINAR

TITLE: Dimension theory and linear continuous surjective mappings between Cp(X)-spaces

SPEAKER: Arkady Leiderman, Ben-Gurion University of the Negev, Beer Sheva, Israel

TIME: 2:30pm – 3:20pm

ROOM: Ayres 114

We consider the space Cp(X) of continuous real-valued functions on a Tychonoff space X equipped with the topology of point-wise convergence. In the talk we will survey the results obtained towards the solution of the following open problem PROBLEM 1. Characterize compact spaces X such that there exists a continuous linear (linear and open) map from Cp[0,1] onto Cp(X). We will show how the famous Kolmogorov Superposition Theorem is relevant to the existence of continuous linear surjections between Cp(X)-spaces.

PROBLEM 2. Let X and Y be Tychonoff spaces and suppose that there exists a linear continuous surjection from Cp(X) onto Cp(Y). Is it true that dim X = 0 implies that dim Y = 0? In a recent paper with Kazuhiro Kawamura we solved PROBLEM 2 positively assuming that X and Y are compact spaces. Our proof is based on the spectral theorem of Shchepin which allows to reduce the problem to the case of compact metrizable spaces.

MATH BIOLOGY SEMINAR

TITLE: Invasions in a Multispecies System

SPEAKER: Cara Sulyok, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres G003

**Wednesday, October 5th **

ANALYSIS SEMINAR

TITLE: Parametric Families of Commuting Squares

SPEAKER: Chase Worley, UTK

TIME: 2:30pm-3:20pm

ROOM: Ayres 003

We investigate analytic deformations of commuting squares arising from finite groups G. In the case G=Z_n, the associated commuting square corresponds to the Fourier matrix of size n, and its deformations correspond to n x n complex Hadamard matrices. This allows us to find deformations of the Fourier matrix in the manifold of complex Hadamard matrices, which is rare and usually hard to do.

Since we want to construct families of commuting squares, we will look at the direction in which they might converge. To do this, we will construct a basis of the tangent space of the commuting square. Then we will examine which directions in the tangent space yield analytic deformations. In doing so, we will be able to create multi-parametric families of commuting squares, and thus multi-parametric families of complex Hadamard matrices containing the Fourier matrix. Our work builds on the previous work of Nicoara and White.

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR - cancelled

TITLE: TBA

SPEAKER: Cory Hauck, ORNL/UTK

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

*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:**