Northeastern University, Department of Mathematics
Organizers: Paul Hand, Ken Duffy, Adam Ding, He Wang
*For remote/hybrid meetings, Zoom/Teams link will be sent by email. Contact He Wang at he.wang@northeastern.edu
The seminar features talks in Applied and Interdisciplinary Mathematics (AIM) by our own faculty as well as faculty from other departments at Northeastern and other Universities. For additional information or to be added to the mailing list, please contact He Wang.
Incoming Talks
| Date: Wednesday, December 6, 2023 Time: 1:30-2:30 pm Location: 509/511 Lake Hall Speaker: Aditya Gopalan ( UIUC) Title: On an Asymptotic Criterion for Blockchain Design Abstract: The salient feature of blockchains is the use of a stochastic growth process to generalize the notion of consensus in the classical Byzantine Generals Problem. In this talk, we introduce the Asynchronous Composition Model to study a sequence of random graphs growing according to blockchain dynamics. The term “asynchronous” refers to the fact that our updates take the form $X_t =X_{t-1} \cup f( X_{t – \xi_t})$, where $\xi_t$ is random, and $f$ randomly adds a single vertex to the graph. We discuss the limiting behavior of asynchronous composition as time goes to infinity. Our main focus is the one-endedness of the limit random graph, which is a precise statement of the notion that the limit graph “only grows to infinity in one direction.” One-endedness is a key property for ensuring the consensus dynamics in a blockchain. In particular, we establish one-endedness for the Nakamoto rule, the canonical choice in protocols like Bitcoin, and the $f_2$ rule from the Iota protocol, the most non-trivial rule used in a widely adopted blockchain protocol. Bio of the speaker: Aditya Gopalan is a PhD student in the Industrial and Enterprise Systems Engineering Department at the University of Illinois Urbana-Champaign. He is advised by Partha Dey. He is broadly interested in applied probability, with a current methodological focus on point process dynamics, stochastic growth processes, and stochastic recursive sequences with random delays. Some applications of his interest include blockchains, opinion dynamics, first-passage percolation, and queueing. Aditya received his bachelor’s degree from MIT in 2018. This talk is jointly hosted with Northeastern Mathematics Graduate Students Seminar |
Past Talks in 2023
| Date: Tuesday, November 28, 2023 Time: 3-4 pm Location: ISEC Room 432 (Northeastern University Interdisciplinary Science and Engineering Complex) Speaker: Thierry Mora (École Normale Supérieure in Paris) Title: Propagating waves of immune-virus coevolution Abstract: Fast-evolving viruses and immune systems play an evolutionary game of cat and mouse. Viruses thrive upon escaping the hosts’ immunity, while the hosts’ immune systems collectively track the virus. I will show how a theory of this process predicts the emergence of solitary propagating waves in antigenic space, and suggests new insights into the evolution of mutability and virulence. I will also discuss some data analysis of virus and antibody repertoires of HIV patients supporting in-host immune-viral co-evolution. Bio of the speaker: Thierry Mora got his PhD from the University of Paris-Saclay on the statistical physics of random optimization problems. During his postdoc in Princeton he got closer to questions related to biology. Since 2010 he has been a permanent researcher at the Ecole normale supérieure in Paris, where he works on a variety of topics from biophysics to neuroscience, collective behaviour, and immunology, applying tools from physics and statistical inference to biological data, and where he teaches as an attached Professor. He is presently a visiting scientist at the University of Chicago. This talk is jointly hosted with faculty from the Center for Theoretical Biological Physics and the Department of Bioengineering. |
| Date: 3-4 pm, Tuesday, April 18, 2023 in 511 Lake and by Teams (Hybrid) Speaker: Kaifeng Bu (Harvard University) Title: Magic from a quantum convolutional approach Abstract: Stabilizer states and Clifford unitaries have played important roles in quantum information and computation, such as quantum error correcting code and measurement-based quantum computation. In this work, I will introduce a convolutional framework to study stabilizer states and channels based on qudits. Moreover, we establish a quantum central limit theorem, based on iterating the convolution of a quantum state, and show this converges to a stabilizer state. This talk is based on the joint work with Weichen Gu, and Arthur Jaffe (arXiv:2302.07841, 2302.08423). |
| Date: 3-4 pm, Thursday, March 30, 2023 in 105 Shillman and by Zoom ( Note unusual day, time, and location) Speaker: Stuart Brorson (Northeastern University) Title: Anomaly Detection using Linear Algebra Abstract: Detecting anomalous events in time series is an important new application for computers. For example, if a problematic squeak or a rumble emitted by an industrial motor could be caught and repaired early, potentially millions of dollars of repair costs may be avoided. I will outline a simple anomaly detection algorithm which uses the Fourier Transform and methods drawn from Linear Algebra. I will demonstrate the algorithm running on a Beaglebone single-board computer and some inexpensive electronics. This talk will be accessible to undergrads and anybody interested in applications of applied math. |