Spring 2024 Colliquia
February 2, 2024
Tom Roby, University of Connecticut
Dynamical algebraic combinatorics: Actions, orbits, and averages
Time: 4:00 pm
Location: JCC 270
Reception: JCC 501 5:00 pm
Abstract: Dynamical algebraic combinatorics explores maps on sets of discrete combinatorial objects with particular attention to their orbit structure. Interesting counting questions immediately arise: How many orbits are there? What are their sizes? What is the period of the map if it's invertible? Are there any interesting statistics on the objects that are well-behaved under the map? One particular phenomenon of interest is “homomesy'', where a statistic on the set of objects has the same average for each orbit of an action. Along with its intrinsic interest as a kind of hidden “invariant'', homomesy can be used to help understand certain properties of the action. Proofs of homomesy often lead one to develop tools that further our understanding of the underlying dynamics, e.g., by finding an equivariant bijection. These notions can be lifted to higher (piecewise-linear, birational, and even noncommutative) realms, of which the combinatorial situation is a discrete shadow, and the resulting identities are somewhat surprising. Maps that can be decomposed as products of “toggling'' involutions are particularly amenable to this line of analysis. This talk will be an introduction to these ideas, giving a number of examples.
March 1, 2024
Jose Perea, Northeastern University
The Underlying Topology of Data
Time: 4:00 pm
Location: JCC 270
Reception: JCC 501 5:00 pm
Abstract: Topology is the branch of mathematics concerned with shapes and their spatial properties. In this talk I’ll show how several ideas from classic algebraic topology – like cohomology, classifying spaces and vector bundles – can be used in machine learning tasks such as dimensionality reduction, time series analysis and data alignment.
April 5, 2024
Susan Landau, Fletcher School and Computer Science Department, Tufts University
The Shape-Shifting Crypto Wars
Time: 4:00 pm
Location: Anderson 206
Reception: JCC 501 5:00 pm
Abstract: The US government and cryptographers, industry, and academia faced off beginning in the 1970s about the private sector's right to develop encryption for business and public use. By the 1990s, the battle had transformed into industry's ability to sell devices with strong encryption, with the US government using export controls to control the technology's use. In 2000, the government substantively loosened export controls, but industry deployment was slow --- until the Snowden disclosures. When Apple, Google, Meta and other companies began efforts to provide easy-to-use and widely available consumer encryption products, the FBI went into full-force battle. Clashes in the First Crypto Wars were over the use of easily available encryption by terrorists, drug dealers, and organized crime, but now the battlefield has become one over Child Sexual Abuse Material. This talk will dissect the ever-shifting Crypto Wars and explain why (parts of) the US government have the issue wrong---again. Susan Landau is Bridge Professor of Cyber Security and Policy at The Fletcher School and School of Engineering, Department of Computer Science at Tufts. She is the founding director the MS program in Cybersecurity and Public Policy at The Fletcher School and School of Engineering. She is the recipient of the 2024 AMS Bertrand Russell Prize and co-recipient of the 2023 USENIX Lifetime Achievement Award. She holds a BA from Princeton, MS from Cornell, and PhD in applied math/theoretical computer science from MIT.
Martin Guterman Lecture 2024
April 26, 2024
Dr. Fern Hunt, Researcher, National Institute of Standards and Technology
A Random Walk Approach to Communication in Networks
Time: 4:00 pm
Location: JCC 270
Reception: JCC 535 5:00 pm
Abstract: The speaker will discuss a very simple but popular random walk description of communication in a social network known as a consensus model. An individual in the network as represented by a vertex, is connected by edges to other vertices representing members the individual communicates with. Suppose one seeks to spread a message throughout the entire network, by initially telling just a few members. Given constraints on the cardinality, what subset of nodes should be selected so the message spreads to the rest of the network at the fastest rate? We will describe an approach to this difficult problem that uses a combination of discrete optimization and age mixing theory of finite Markov chains to identify optimal and close to optimal subsets.
Biography: Fern Hunt is scientist emeritus and mathematician at the National Institute of Standards and Technology (NIST) in Gaithersburg Maryland. She holds an A.B. in Mathematics from Bryn Mawr College, and MS and PhD degrees in Mathematics from the Courant Institute at New York University. Prior to joining NIST, she taught at City College of New York, the University of Utah, and Howard University. She has given invited addresses at AMS, SIAM, and MAA meetings, is a recipient of an Arthur S. Flemming Award for Outstanding Federal Service in Science, and was given special honors by the Chicago Museum of Science and Industry. For her research, mentoring, and service, Dr. Hunt was named a Fellow of the American Mathematical Society and a Fellow of the Association for Women in Mathematics.