**Seminars and Colloquiums**

for the week of October 26, 2015

for the week of October 26, 2015

*SPEAKER:*

Vajira Manathunga, UTK, Monday

Mark Bly, UTK, Monday

Faith Celiker, Wayne State University, Thursday

Andrew Belt, UTK, Thursday

Jordan Bush, UTK, Friday

Chase Worley, UTK, Friday

Qiang Du, Columbia University, Friday

*Tea Time, Monday - Wednesday, 3:00 pm*

Hosted by Bonnie, Cara, & Tricia

Hosted by Bonnie, Cara, & Tricia

**Monday October 26**

GEOMETRY/TOPOLOGY SEMINAR

TITLE: Extracting integer invariants from a power series expansion of the Jones polynomial

TIME: 2:30 – 3:20pm

ROOM: Ayres 114

SPEAKER: Vajira Manathunga (UTK)

Abstract: It is known that appropriate change of variable of Jones polynomial followed by Taylor series expansion gives an infinite power series with coefficients that are Vassiliev invariants. However these Vassiliev invariants are rational valued. We can convert them to integer valued Vassiliev invariants by multiplying it with appropriate constant $\lambda_k$. In this talk we give a formula for minimal $\lambda_k$ when $k$ is even.

ALGEBRA SEMINAR

TITLE: Projective modules and Hermite rings

TIME: 3:35 – 4:25pm

ROOM: Ayres 114

SPEAKER: Mark Bly, UTK

Abstract: This and the next few talks explain Suslin's proof of Serre's conjecture on projective modules.

**Tuesday October 27**

STOCHASTICS SEMINAR -- Canceled

**Wednesday October 28 **

COMPUTATIONAL & APPLIED MATHEMATICS (CAM) SEMINAR -- Canceled

** Thursday October 29**

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Incorporating local boundary conditions into nonlocal theories

TIME: 2:10 – 3:25pm

ROOM: Ayres 114

SPEAKER: Faith Celiker, Wayne State University

Abstract: We study nonlocal wave equations on bounded domains related to peridynamics. We generalize the standard integral based convolution to an abstract convolution operator defined by a Hilbert basis. This operator is a function of the classical operator which allows us to incorporate local boundary conditions into nonlocal theories. We present a numerical study of the solutions. For discretization, we employ a weak formulation based on a Galerkin projection which allows discontinuities on element boundaries

JUNIOR COLLOQUIUM

TITLE: Algebra in Cryptography

TIME: 3:40 – 4:30pm

ROOM: Ayres 405

SPEAKER: Andrew Belt, UTK

Abstract: Group theory is the foundation of most modern cryptographic algorithms used on the Internet and in mobile communications. As computers become faster, parties can increase the power of their cryptography, usually resulting in a larger underlying group. As this power is increased, encryption and decryption become slower, but cracking the system often takes exponentially more time, so a balance of security and convenience can always be reached. However, in the near future, the quantum model of computation may break this balance, allowing security to be compromised in approximately the same time as encrypting the message. Thus there is motivation for developing new systems of cryptography based on more exotic groups with the goal of making encryption fast on classical computers and attacks hard on both computation models. A broad overview of classical cryptography and their known attacks will be given, in addition to lesser-known alternative methods.

**Friday October 30**

MATH BIOLOGY SEMINAR

TITLE: Social personality polymorphism and the spread of invasive species: a model (paper by Fogarty et al).

TIME: 10:10 – 11:00am

ROOM: Ayres 405

SPEAKER: Jordan Bush, UTK

ANALYSIS SEMINAR

TITLE: Circulant Core Hadamard Matrices, Part II

TIME: 2:30- 3:20pm

ROOM: BU 476

SPEAKER: Chase Worley, UTK

Abstract: This is a continuation of my previous talk. We will begin by discussing Hadamard matrices with both real and complex entries. After dephasing a Hadamard matrix, we can examine the properties of the core of the matrix. We investigate the Hadamard matrices whose core is circulant. We give examples coming from Number Theory. Then we prove a finiteness result for circulant core Hadamard matrices of size p+1 when p is a prime number.

COLLOQUIUM AND HOUSEHOLDER DISTINGUISHED LECTURE

TITLE: Application of Householder transform to transition state search

TIME: 3:35 -4:25pm

ROOM: Ayres 405

SPEAKER: Qiang Du, Columbia University

Abstract: Finding transition states on a complex energy landscape is an interesting computational problem that appears in many applications. This lecture will discuss how Householder transform plays a useful role in the design of robust algorithms for effective transition state search. Rigorous mathematical analysis of such algorithms will be presented along with some discussion on various applications.

*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 *