- You are here:
- GT Home
- Home
- News & Events

Series: Research Horizons Seminar

Hosted by: Huy Huynh and Yao Li

We will have a chance to spend some time together to discuss issues
of relevance to the Graduate Program. Sort of like a "Town Hall
Meeting" of the graduate students and the graduate coordinator.
There are some things that I need to communicate to all of you,
but the format is otherwise unstructured, and I am seeking suggestions
on things which you would like to see addressed. So, please send me
comments on things which you would like to see discussed and I will
do my best to get ready for them.
Thanks, Luca Dieci.

Series: Research Horizons Seminar

Hosted by: Huy Huynh and Yao Li

The Scenery Reconstruction Problem consists in trying to reconstruct
a coloring of the integers given only the observations made by
a random walk. For this we consider a random walk S and
a coloring of the integers X. At time $t$ we observe
the color $X(S(t))$. The coloring is i.i.d. and we show that
given only the sequence of colors
$$X(S(0)),X(S(1)),X(S(2)),...$$
it is possible to reconstruct $X$ up to translation
and reflection. The solution depends on the property of the
random walk and the distribution of the coloring.
Longest Common Subsequences (LCS) are widely used in genetics.
If we consider two sequences X and Y, then a common subsequence
of X and Y is a string which is a subsequence of X and of Y at the same
time. A Longest Common Subsequence of X and Y is a common
subsequence of X and Y of maximum length. The problem of the asymptotic
order of the flucutation for the LCS of independent random
strings has been open for decades. We have now been able to
make progress on this problem for several important cases.
We will also show the connection to the Scenery Reconstruction
Problem.

Series: Research Horizons Seminar

Hosted by: Huy Huynh and Yao Li

The Hilbert transform is a foundational transform, with deep connections to
electrical charge, and analyticity. The `two weight inequality for the
Hilbert transform' concerns the most general setting in which the Hilbert
transform admits a (weighted) L^2 inequality. We will give a couple of
(surprising?) ways that this question arises. And we will indicate the
surprise that is behind the recent description of all setting in which the
two weight inequality holds.

Series: Research Horizons Seminar

Hosted by: Huy Huynh and Yao Li

Sampling from and approximately counting the size of a large set
of combinatorial structures has contributed to a renaissance in research
in finite Markov chains in the last two decades.
Applications are wide-ranging from sophisticated card shuffles,
deciphering simple substitution ciphers (of
prison inmates in the California state prison), estimating the volume of
a high-dimensional convex body,
and to understanding the speed of Gibbs sampling heuristics in
statistical physics. More recent applications include rigorous estimates
on J.M. Pollard's (1979) classical Rho and Kangaroo algorithms for the
discrete logarithm problem in finite cyclic groups.
The lecture will be a brief (mostly self-contained) introduction to the
Markov Chain Monte Carlo (MCMC) methodology and applications, and will
include some open problems.

Series: Research Horizons Seminar

Hosted by: Huy Huynh and Yao Li

Orthogonal Polynomials and their generalizations have a great many
applications in areas ranging from signal processing to random matrices
to combinatorics. We outline a few of the connections, and present some
possible Ph. D Problems

Series: Research Horizons Seminar

Hosted by: Huy Huynh and Yao Li

Olof Sisask and myself have produced a new probabilistic
technique for finding `almost periods' of convolutions of subsets of
finite groups. In this talk I will explain how this has allowed us
to give (just recently) new bounds on the length of the longest
arithmetic progression in a sumset A+A.

Series: Research Horizons Seminar

Hosted by: Huy Huynh and Yao Li

I will discuss some theorems and conjectures in the relatively new
field of arithmetic dynamics, focusing in particular on some methods
from number theory which can be used to study the orbits of points in
algebraic dynamical systems.

Series: Research Horizons Seminar

Hosted by: Huy Huynh and Yao Li

In the preceeding talk, I outlined a framework for variational problems
and some of the basic tools and results. In this talk I will attempt
describe several problems of current interest.

Series: Research Horizons Seminar

I will describe several geometrical problems that arise from
the minimization of some sort of integral functional and the basic
relation between such minimization and partial differential equations.
Then I will make some further comments on my favorite kind of such
problems, namely those that have something to do with minimizing area of
surfaces under various side conditions.

Series: Research Horizons Seminar

The Research Horizons seminar this week will be a panel discussion on
the academic job market for mathematicians. The discussion will begin
with an overview by Doug Ulmer of the hiring process, with a focus on
the case of research-oriented universities. The panel will then take
questions from the audience. Professor Wick was hired last year at
Tech, so has recently been on the students' side of the process.
Professor Harrell has been involved with hiring at Tech for many years
and can provide a perspective on the university side of the process.