School Seminars and Colloquia

Previous Colloquia

• 2019 Colloquia

  Sept. 11, 2019: “Phylogenetic Algebraic Geometry,” Seth Sullivant, NC State University.

  ABSTRACT: The main problem in phylogenetics is to reconstruct evolutionary relationships between collections of species, typically represented by a phylogenetic tree. In the statistical approach to phylogenetics, a probabilistic model of mutation is used to reconstruct the tree that best explains the data (the data consisting of DNA sequences from homologous genes of the extant species). In algebraic statistics, we interpret these statistical models of evolution as geometric objects in a high-dimensional probability simplex. This connection arises because the functions that parametrize these models are polynomials, and hence we can consider statistical models as algebraic varieties. The goal of the talk is to introduce this connection and explain how the algebraic perspective leads to new theoretical advances in phylogenetics, and also provides new research directions in algebraic geometry. The talk material will be kept at an introductory level, with background on phylogenetics and algebraic geometry.

  BIO: Seth Sullivant received his Ph.D. in 2005 from the University of California, Berkeley. After a junior fellowship in Harvard’s Society of Fellows, he joined the Department of Mathematics at North Carolina State University in 2008 as an assistant professor. He was promoted to full professor in 2014 and distinguished professor in 2018. Sullivant’s work has been honored with a Packard Foundation Fellowship and an NSF CAREER award and he was selected as a Fellow of the American Mathematical Society. He helped found the SIAM activity group in Algebraic Geometry where he has served as both secretary and chair. Sullivant’s current research interests include algebraic statistics, mathematical phylogenetics, applied algebraic geometry, and combinatorics.

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  March 28, 2019: Space, Time and Big Data: How Bayesian Modeling Can Tackle Challenges in Modern Data Science,” Sudipto Banerjee, UCLA Biostatistics.

  ABSTRACT: Per the speaker: In this talk, I will attempt to provide a broad overview of the challenges in statistical inference posed by spatial-temporal big data arising in the sciences. The essential underlying theme will be to exemplify how we might be able to “model our way out of trouble” by overcoming the major computational bottlenecks faced in the statistical analysis of big data. I will provide some examples of approaches that scale up to massive datasets without requiring massive storage or computations while at the same time not throwing away or ignoring any part of the data. The talk will be delivered at a fairly nontechnical level and focus upon several recent examples of big data analytics for spatial-temporal datasets.

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  March 13, 2019: “Galois Groups in Enumerative Geometry and Applications,” Frank Sottile, math, Texas A&M.

  ABSTRACT: In 1870, Jordan explained how Galois theory can be applied to problems from enumerative geometry, with the group encoding intrinsic structure of the problem. Earlier Hermite showed the equivalence of Galois groups with geometric monodromy groups, and in 1979 Harris initiated the modern study of Galois groups of enumerative problems. He posited that a Galois group should be `as large as possible’ in that it will be the largest group preserving internal symmetry in the geometric problem. I will describe this background and discuss some work in a long-term project to compute, study, and use Galois groups of geometric problems, including those that arise in applications of algebraic geometry. A main focus is to understand Galois groups in the Schubert calculus, a well-understood class of geometric problems that has long served as a laboratory for testing new ideas in enumerative geometry.

• 2018 Colloquia

  March 2, 2018: “What is Weak KAM Theory?” Albert Fathi, Georgia Tech.

  ABSTRACT: The goal of this lecture is to explain and motivate the connection between Aubry-Mather theory (dynamical systems), and viscosity solutions of the Hamilton-Jacobi equation (PDE). This connection is the content of weak KAM Theory. The talk should be accessible to all mathematicians. No prior knowledge of any of the two subjects is assumed.

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  Jan. 16, 2018: “On the Geometry of the Simplex Method and other Simplex-like Linear Optimization Algorithms,” Jesus De Loera, UC Davis

  ABSTRACT: Linear programs and their associated convex polyhedra are, without any doubt, at the core of both the theory and the practice of mathematical optimization (e.g., in discrete optimization LPs are used in practical computations using branch-and-bound, and in approximation algorithms, e.g., in rounding schemes). Despite their key importance, many simple easy-to-state mathematical properties of LP and their polyhedra remain unknown. My talk overviews the state of the art about the computational complexity of the famous simplex method and some recent variations. All results are joint work with S. Borgwardt, E. Finhold, Raymond Hemmecke, and Jon Lee.

• 2016 Colloquia

  March 10, 2016: “A Rotator’s View of the NSF: Everything You Ever Wanted To Know About The NSF (But Were Afraid To Ask),” Amnon Meir.

  ABSTRACT: During the first part of the talk I will provide an overview of the NSF and, in particular, MPS/DMS from the perspective of a faculty rotator. I will also describe proposal handling (by the NSF), the merit review process, and suggest some "dos and don’ts" when preparing and submitting a proposal. I will devote the second part of the talk to answering your questions about the NSF, DMS, and the review process (even those you were/are afraid to ask, so please come prepared).

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  March 28, 2016: “Title: The Flight of the Smallest Insects,” Laura Miller, UNC Chapel Hill.

  ABSTRACT: A vast body of research has described the complexity of flight in insects ranging from the fruit fly, Drosophila melanogaster, to the hawk moth, Manduca sexta. The smallest flying insects have received far less attention, although previous work has shown that flight kinematics and aerodynamics can be significantly different. In this presentation, three-dimensional direct numerical simulations and experiments with dynamically scaled robotic insects are used to compute the lift and drag forces generated by flexible and/or bristled wings to reveal the aerodynamics of these tiny fliers. An adaptive version of the immersed boundary method is used to simulate simplified flexible wings in pure translation, rotation, and performing a ‘clap and fling’ maneuver. Results are validated against dynamically scaled physical models using particle image velocimetry. At the lowest Reynolds numbers relevant to tiny insect flight, the ratio of lift to drag forces decreases. For Reynolds numbers below 10, the relative forces required to rotate the wings and perform “clap and fling” become substantially greater. Wing flexibility and bristles can reduce the drag forces necessary to fling the wings apart while increasing the peak and average lift forces produced during the stroke.

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  March 30, 2016: “ARock: an Asynchronous Parallel Algorithmic Framework,” Wotao Yin, UCLA.

  ABSTRACT: The performance of the CPU core stopped improving around 2005. Moore’s Law, however, continues to apply — not to the single-thread performance — but the number of cores in each computer. Today, at affordable prices, we can buy 64 CPU-core workstations, thousand-core GPUs, and even eight-core cellphones. To take advantages of multiple cores, we must parallelize our algorithms. Otherwise, our algorithms won’t run any faster on newer computers. For iterative parallel algorithms to have the strong performance, asynchrony is critical. Removing the synchronizations among different cores will eliminate core idling and reduce memory-access congestions. However, some of those cores may no longer compute with the latest information. We study fixed-point iterations with out-of-date information and show that randomized async-parallel iterations of a nonexpansive operator will almost surely converge to a fixed point, provided that a fixed point exists and the step size is properly chosen. As special cases, novel algorithms for linear equation systems, machine learning, distributed and decentralized optimization are introduced, and numerical performance will be presented for sparse logistic regression and others. This is joint work with Zhimin Peng (UCLA), Yangyang Xu (IMA), and Ming Yan (Michigan State).

• 2015 Colloquia

  Dec. 1, 2015: “Computational Models and Challenging Global Optimization Problems,” Panos Pardalos.

  ABSTRACT: Most of the conventional computer models are based on the von Neumann computer architecture and the Turing machine model. However, quantum computers (several versions), analog computers, DNA computers and several other exotic models have been proposed in an attempt to deal with intractable problems. We are going to give a brief overview of different computing models and discuss several classes of optimization problems that remain very difficult to solve. Such problems include graph problems, nonlinear assignment problems, and global optimization problems. We will start with a historical development and then we will address several complexity and computational issues. Then we are going to discuss heuristics and techniques for their evaluation.

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  March 23, 2015: “The Euclidean Distance Degree,” Bernd Sturmfels

  ABSTRACT: The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. The Euclidean distance degree is the number of critical points for this optimization problem. We focus on projective varieties seen in engineering applications, and we discuss tools for exact computation. Our running example is the Eckart-Young Theorem which relates the nearest point map for low rank matrices with the singular value decomposition. This is joint work with Jan Draisma, Emil Horobet, Giorgio Ottaviani and Rekha Thomas.