Department of Mathematics
The Mathematics Department Colloquium typically meets on Thursdays from 12:20 pm to 1:10 pm in NAC 6/113, with lunch immediately after.
Thursday, March 30, 2017, 01:00PM, NAC 6/113Amie Wilkinson (U of Chicago), A dynamical way of thinking
The modern mathematical field of Dynamical Systems encompasses a wide range of subdisciplines and techniques. As its scope spreads into more and more areas of mathematics, one is led to redefine Dynamical Systems as a mode of thought, an approach to problem solving. I'll illustrate how a dynamical way of thinking can be applied in a variety of contexts, and how it informs our current perspective.
(AWM/Math Club Undergraduate Colloquium)
Tuesday, April 04, 2017, 12:30PM, NAC 6/310Prof. Hillel Furstenberg (Hebrew University of Jrusalem), Ergodic Ramsey Theory for Non-amenable Groups
Ramsey theory treats the phenomenon that certain patterns must appear inside sufficiently large subsets of structures of a certain type. The prototype is the assertion conjectured by Erdos and Turan and proved by Szemeredi, that a subset of the integers with positive density possesses arbitrarily long arithmetic progressions. This has an ergodic-theoretic proof based on recurrence patterns that show up in any ergodic dynamical system. One can ask for similar phenomena for "large" subsets of other groups. It is not difficult to generalize the "dynamic" approach to amenable groups because of the existence of an invariant density notion. We show that for arbitrary group actions there is a notion of measures invariant "on the average". With this we can define the analogue of subsets of positive density and prove a general version of the following: If a subset of a finitely generated free group has the property that for every sufficiently large L, it contains a fixed positive proportion of all words of length L, then it contains geometric progressions of every length.
Thursday, April 27, 2017, 12:20PM, SH-205Steve Smale (University of California at Berkeley), A life in mathematics-pure and applied
My 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.
Thursday, May 11, 2017, 12:20PM, NAC 6/113Phil Kutzko (University of Iowa), The Math Alliance: partnering with faculty in the NYC Metropolitan Area to build a new, inclusive, community in the mathematical sciences
The 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 – F-GAP – 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, May 18, 2017, 12:20PM, NAC 6/113Basilis Gidas (Brown University), TBA
Most recent talks
Thursday, March 23, 2017, 12:20PM, NAC 6/113Thomas Koberda (University of Virginia), Square roots of Thompson's group F
I will discuss square roots of Thompson's group F, which are certain two-generator subgroups of the homeomorphism group of the interval, the squares of which generate a copy of Thompson's group F. We prove that these groups may contain non-abelian free groups, they can fail to be smoothable, and can fail to be finitely presented. This represents joint work with Y. Lodha.
Thursday, March 02, 2017, 12:20PM, NAC 6/113Katharina Huber ( University of East Anglia, UK), Orthology relations: From trees to networks
Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple relations on a set of sequences called orthology relations may be employed. In addition to being interesting from a practical point of view, they are also attractive from a theoretical perspective in that e.g. a characterization is known for when such a relation is representable by a certain type of phylogenetic tree. A natural approach to overcome the problem that real biological data hardly ever satisfies that characterization might be to correct the data in some way or another. Recent work however suggests that this approach has major drawbacks. Starting with a brief introduction into the area of phylogenetic networks and trees, we present recent results concerning the use of such networks (as opposed to phylogenetic trees) for representing orthology relations.
Thursday, December 01, 2016, 12:20PM, NAC 6/113Enrique Pujals (Instituto Nacional de Matemática Pura e Aplicada), Back and Forth on the Lorenz Attractor: Hitchhiking on Geometrical Construction
Almost five decades ago, E. Lorenz published an article in the Journal of Atmospheric Sciences, which raised mathematical questions that played an essential role in the modern development of the theory of dynamical systems. I will make an effort to describe this ride.