Un of Tenn | Math Department

Seminars and Colloquiums
for the week of April 9, 2012

Speaker:

Mr. Nathan Pollesch and Ms. Sara Abdelmageed, Monday
Ms. Ashley Rand, Monday
Ms. Beth Lewis, Monday
Mr. Vajira Manathunga, Wednesday
Dr. Victor Perez-Abreu, Center for Research in Mathematics, CIMAT, Mexico, Wednesday
Dr. Daniel Fiorilli, IAS, Thursday
Dr. Daniel Fiorilli, IAS, Friday

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. Judy Day.

Monday, April 9

MATH BIOLOGY SEMINAR
TIME: 12:45 – 1:35 p.m.
ROOM: Ayres 121
SPEAKER: Nathan Pollesch and Sara Abdelmageed
TITLE: Introduction of Agent-based Models (part 3)

TOPOLOGY SEMINAR
TIME: 2:30 – 3:20 p.m.
ROOM: Ayres G004
SPEAKER: Ms. Ashley Rand
TITLE: The Zariski Topology - 2
ABSTRACT: Let R be a commutative ring with spec(R) its set of prime ideals. We discuss a topology on spec(R) called the Zariski topology and some of the basic properties.

ALGEBRA SEMINAR
TIME: 3:35 - 4:25 p.m.
ROOM: Ayres B004
SPEAKER: Ms. Beth Lewis
TITLE: The zero-divisor graph of a commutative semigroup? (continued)
ABSTRACT: Let S be a commutative semigroup with 0. The zero-divisor graph of S is the simple graph with vertices the nonzero zero-divisors of S and two distinct vertices x and y are adjacent if xy = 0. We will discuss some properties of this graph.

Wednesday, April 11

TOPOLOGY SEMINAR
TIME: 2:30 p.m. - 3:20 p.m.
ROOM: Ayres Hall G004
SPEAKER: Mr. Vajira Manathunga
TITLE: Upper bounds on the number of linearly independent Vassiliev invariants
ABSTRACT: After briefly introducing the concept of Vassiliev knot invariants, we will outline an argument of Chmutov and Duzhin giving an upper bound on the number of independent invariants in each degree.

JOINT ANALYSIS AND PROBABILITY SEMINAR
TIME: 3:35 pm
ROOM: Ayres 112
SPEAKER: Dr. Victor Perez-Abreu, Center for Research in Mathematics, CIMAT, Mexico
TITLE: Free Convolutions in Free Probability
ABSTRACT: In the 1980s Dan Voiculescu introduced the notion of free independence in noncommutative probability theory, which emerged from his seminal works on operator algebras associated to the free group factors. He also considered the concepts of free additive and multiplicative convolutions as the spectral distributions of the sum and the product of freely independent noncommutative random variables. Motivation as well as some of the major applications of such convolutions are in the theory of large-dimension random matrices.

The purpose of this talk is to present a general overview of the analytic approach to the free additive and multiplicative convolutions and their parallelism to the classical convolutions of probability measures. The role of the Cauchy transform is shown, which plays a similar role the Fourier transform does in classical convolution.

This is the first part of the lecture series on "Free Probability, Random Matrices and Infinite Divisibility". Part II: Random matrices and Part III: Infinite divisibility will be given on Probability Seminars, April 16 and 23rd.

Thursday, April 12

JUNIOR COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 405
SPEAKER: Dr. Daniel Fiorilli, IAS
TITLE: Races between prime numbers
ABSTRACT: In a 1853 letter to Fuss, Chebyshev made the remark that there seems to be more primes of the form 4n+3 than of the form 4n+1. If we compute the (normalized) difference between these two kinds of primes up to x, and make a graph of this quantity with x varying, then we get the figure which is shown here. What one remarks is that the difference is almost always positive, confirming Chebyshev's assertion. Interestingly, the statement in Chebyshev's letter is equivalent to the Riemann hypothesis for a certain zeta function; in fact the whole subject of prime number races is highly dependent on the zeros of zeta functions. The goal of the present talk will be to give a taste of the subject, focusing on the amusing facts.

Pizza will be available at 3:15 p.m.

Friday, April 13

COLLOQUIUM
TIME: 3:35 – 4:25 pm
ROOM: Ayres 405
SPEAKER: Dr. Daniel Fiorilli, IAS
TITLE: Nuclear physics and number theory
ABSTRACT: While the two fields named in the title seem completely unrelated, there is a very strong link between them. Indeed, random matrix theory makes tremendous predictions in both fields, and some of these predictions can be verified rigorously on the number theory side. This amazing connection came to life during a meeting between Freeman Dyson and Hugh Montgomery at the Institute for Advanced Study. Random matrices are now known to predict many statistics about zeta functions, such as moments, low-lying zeros and correlations between zeros. The goal of this talk is to discuss this connection, focusing on number theory. We will cover both basic facts about the zeta functions and recent developments in this very active area of research.

Refreshments will be available in Ayres 401 at 3:15 p.m.

Past notices:

4_2_12.html

3_26_12.html

March 19, 2012 - spring break