Department of Mathematics
Mathematics Colloquium
OrganizerThe Mathematics Department Colloquium typically meets on Thursdays from 12:30 pm to 1:20 pm in NAC 6/111, with lunch immediately after.
Upcoming talks

Thursday, October 19, 2017, 12:30PM, NAC 6/111
Eli Glasner ( TelAviv University), On the disjointness property of groupsIn his seminal 1967 paper "Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation" Furstenberg introduced the notion of disjointness of dynamical systems, both topological and measure preserving. In this paper he showed, among many other beautiful results, that for the integers the Bernoulli system is disjoint from every minimal system, and then applied this approach to prove his famous Diophantine theorem: If S is a nonlacunary semigroup of integers and a is an irrational, then Sa is dense in the circle R/Z. I will review the development of these ideas during the following decades and introduce a new class of groups, DJgroups, to which the main disjointness results extend. Amenable and residually finite groups are DJ, and the DJ property extends through short ex act sequences. In fact, we don’t know if there is any group which is not DJ. This is a joint work in progress with Benjy Weiss.

Thursday, October 26, 2017, 12:30PM, NAC 6/111
John Goodrick (Los Andes University, Colombia ), Counting integer points in polytopes with an extension of Presburger arithmeticFix some polytope P in R^d whose vertices have integer coordinates. Then for any positive integer t, one can ask to compute the number fP(t) of points in the lattice Z^d that lie within the tth dilate of P. By a theorem of Ehrhart, the function fP(t) is always a polynomial. If the vertices of P are rational (i.e. in Q^d instead of Z^d), then the function fP(t) is no longer necessarily polynomial but it is a quasipolynomial: there is a number m and polynomials g1, ..., gm such that fP(t) = g_i(t) whenever t is congruent to i modulo m.
In this talk, we will review the classic theory of Ehrhart polynomials and present a generalization (based on recent joint work with Tristram Bogart and Kevin Woods): if f(t) is the function which counts the number of integer points within a bounded region of R^d which is defined by a formula using addition, multiplication by the parameter t, inequalities, and quantifiers over variables from Z (but not over the domain of the variable t), then f(t) is quasipolynomial for all sufficiently large values of t. We call such families "parametric Presburger families" in analogy with the logical theory of Presburger arithmetic. We will also present some new applications of this result to other combinatorially interesting families of sets of integer points.

Thursday, November 02, 2017, 12:30PM, NAC 6/111
Pierre Berger (University Paris 13), 

Thursday, November 09, 2017, 12:30PM, NAC 6/111
Mrinal Kanti Roychowdhury (The University of Texas Rio Grande Valley), Optimal QuantizationThe basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Though the term 'quantization' is known to electrical engineers for the last several decades, it is still a new area of research to the mathematical community. In my presentation, first I will give the basic definitions that one needs to know to work in this area. Then, I will give some examples, and talk about the quantization on mixed distributions. Mixed distributions are an exciting new area for optimal quantization. I will also tell some open problems relating to mixed distributions

Thursday, December 07, 2017, 12:30PM, NAC 6/111
Peter Winkler (Dartmouth College), 
Most recent talks

Thursday, May 18, 2017, 12:20PM, NAC 6/113
Basilis Gidas (Brown University), Finding Genes and Towards a Mathematical Framework for Artificial Intelligence and Biological SystemsThe first half of the lecture will be on a statistical model for finding genes in the human genome. The model contains two parts: (a) A finite network (graph) which represents the overall architecture of a gene. The vertices in the network represent DNA signals (small patterns) associated with a gene and which are recognized by proteins and enzymes involved in the transcription and translation of genes. The edges of the network correspond to interactions among these signals and represent statistical variability in the architecture across genes; (b) each signal and each part of a gene is a piece of DNA with a random length as well as a random variability of its nucleotide sequence. The second part of the model articulates these variabilities.
The above gene finding procedure is conceptually similar to what is believed to underlie speech recognition whereby recognition involves two types of information: The acoustic signal represented by a concatenation of phonemes, and global regularities articulated by grammars (or syntax). The underpinning process in visual recognition is undoubtedly similar. And so is – many practitioners believe – the functioning of biological processes whereby two principles are at work: physics (biochemistry) and evolution. Physics controls the biochemical interaction of macromolecules, but it is evolution that produced the perfect “code” or “syntactic language” for the collective behavior of genes (Gene Regulatory Networks), or the collective behavior of proteins in Signal Transduction Pathways in cell growth, cell division or immunology. While specific questions and application in speech, vision, and biology have seen impressive advances and have lead to a great deal of mathematical innovation (e.g. modern statistical learning), an underpinning mathematical framework is missing. Though we do not have the framework, we know quite a bit of some of the problems the framework needs to articulate and some of the properties it needs to have. Building on the gene finding process, the second part of the talk will aim at identifying some key sources that makes the information processing in cognition and biology difficult, and hint towards a coherent hierarchical/grammatical framework.

Thursday, May 11, 2017, 12:20PM, NAC 6/113
Phil Kutzko (University of Iowa), The Math Alliance: partnering with faculty in the NYC Metropolitan Area to build a new, inclusive, community in the mathematical sciencesThe National Alliance for Doctoral Studies in the Mathematical Sciences (“Math Alliance”) is a national mentoring community of math sciences faculty working together to ensure that any student from a background that is underrepresented in the mathematical sciences and who has the desire and ability to earn a doctoral degree in a math sciences field will have the opportunity, encouragement, support and mentoring to do so. In order to institutionalize its early success, the Alliance has built a network of Master’s and doctoral programs who have made a commitment to train and mentor students from underrepresented backgrounds and has developed a program – FGAP – which works to place Alliance undergraduate and Master’s students in these programs. In order to ensure that promising undergraduates are attracted to math sciences disciplines regardless of where they attend school, the Alliance is partnering with local faculty to build regional alliances. It is my pleasure to tell you about the history and successes of our Math Alliance on the occasion of the launch of our new NYC Math Sciences Alliance!

Thursday, April 27, 2017, 12:20PM, SH205
Steve Smale (University of California at Berkeley), A life in mathematicspure and appliedMy perspective on the dichotomy of pure and applied mathematics will be discussed. This will be related to my own life as a mathematician, neither pure nor applied; but yet I I feel like a mathematician. I will give examples of scientists who have inspired me, Newton, von Neumann, Watson and Crick, Turing.