## Seminars and Colloquia by Series

Wednesday, February 14, 2018 - 12:10 , Location: Skiles 006 , , Georgia Tech , Organizer:
Some basic problems, notions and results of the Ergodic theory will be introduced. Several examples will be discussed.   It is also  a preparatory talk for the next day colloquium where finite time properties of dynamical and stochastic systems will be discussed rather than traditional questions all dealing with asymptotic in time properties.
Friday, February 2, 2018 - 15:53 , Location: Skiles 006 , , GA Tech , Organizer: Timothy Duff
Some basic problems, notions and results of the Ergodic theory will be introduced. Several examples will be discussed.   It is also  a preparatory talk for the next day colloquium where finite time properties of dynamical and stochastic systems will be discussed rather than traditional questions all dealing with asymptotic in time properties.
Wednesday, January 31, 2018 - 12:10 , Location: Skiles 006 , , GA Tech , Organizer: Timothy Duff
In recent years the problem of low-rank matrix completion received a tremendous amount of attention. I will consider the problem of exact low-rank matrix completion for generic data. Concretely, we start with a partially-filled matrix M, with real or complex entries, with the goal of finding the unspecified entries (completing M) in such a way that the completed matrix has the lowest possible rank, called the completion rank of M. We will be interested in how this minimal completion rank depends on the known entries, while keeping the locations of specified and unspecified entries fixed. Generic data means that we only consider partial fillings of M where a small perturbation of the entries does not change the completion rank of M.
Wednesday, December 6, 2017 - 13:10 , Location: Skiles 006 , , Institute for Defense Analyses , , Organizer:
The Institute for Defense Analyses - Center for Computing Sciences is a nonprofit research center that works closely with the NSA.  Our center has around 60 researchers (roughly 30 mathematicians and 30 computer scientists) that work on interesting and hard problems.  The plan for the seminar is to begin with a short mathematics talk on a project that was completed at IDA-CCS and declassified, then tell you a little about what we do, and end with your questions.  The math that we will discuss involves symbolic dynamics and automata theory.  Specifically we will develop a metric on the space of regular languages using topological entropy.  This work was completed during a summer SCAMP at IDA-CCS.  SCAMP is a summer program where researchers from academia (professors and students), the national labs, and the intelligence community come to IDA-CCS to work on the agency's hard problems for 11 weeks.
Wednesday, December 6, 2017 - 12:10 , Location: Skiles 006 , , GT Math , Organizer:
Four dimensions is unique in many ways. For example $n$-dimensional Euclidean space has a unique smooth structure if and only if $n$ is not equal to  four. In other words, there is only one way to understand smooth functions on $R^n$ if and only if $n$ is not 4. There are many other way that smooth structures on 4-dimensional manifolds behave in surprising ways. In this talk I will discuss this and I will sketch the beautiful interplay of ideas (you got algebra, analysis and topology, a little something for everyone!) that go into proving $R^4$ has more that one smooth structure (actually it has uncountably many different smooth structures but that that would take longer to explain).
Wednesday, November 29, 2017 - 12:10 , Location: Skiles 006 , Chongchun Zeng , Georgia Tech , Organizer:
In this talk, we consider the structure of a real $n \times n$ matrix in the form of $A=JL$, where $J$ is anti-symmetric and $L$ is symmetric. Such a matrix comes from a linear Hamiltonian ODE system with $J$ from the symplectic structure and the Hamiltonian energy given by the quadratic form $\frac 12\langle Lx, x\rangle$. We will discuss the distribution of the eigenvalues of $A$, the relationship between the canonical form of $A$ and the structure of the quadratic form $L$, Pontryagin invariant subspace theorem, etc. Finally, some extension to infinite dimensions will be mentioned.
Wednesday, November 15, 2017 - 12:10 , Location: skiles 006 , Joseph Rabinoff , GT Math , Organizer:
A motivating problem in number theory and algebraic geometry is to find all integer-valued solutions of a polynomial equation.  For example, Fermat's Last Theorem asks for all integer solutions to x^n + y^n = z^n, for n >= 3. This kind of problem is easy to state, but notoriously difficult to solve.  I'll explain a p-adic method for attacking Diophantine equations, namely, p-adic integration and the Chabauty--Coleman method.  Then I'll talk about some recent joint work on the topic.
Wednesday, November 8, 2017 - 12:10 , Location: Skiles 006 , Michael Worthington , GA Tech , Organizer: Timothy Duff
Wednesday, November 1, 2017 - 12:10 , Location: Skiles 006 , Igor Belegradek , GA Tech , Organizer: Timothy Duff
The talk will include a crash course on infinite dimensional topology, with applications to various topological properties of the space of congruence classes of convex bodies in the Euclidean space.
Wednesday, October 18, 2017 - 12:10 , Location: Skiles 006 , Rachel Kuske , Georgia Tech , Organizer:
This talk will cover some recent and preliminary results in the area of non-smooth dynamics, with connections to applications that have been overlooked.   Much of the talk will present open questions for research projects related to this area.