TAGMaC 2019
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Events
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Jeaman Ahn, Kongju National University, Multivariate Hermite Interpolation via Explicit Groebner Basis
Multivariate Hermite interpolation problem asks to find a "small" polynomial that has given values of several partial derivatives at given points. It has numerous applications in science and engineering. Thus, naturally, it has been intensively studied, resulting in various beautiful ideas and techniques. One approach is as follows. (1) Chooses a basis of the vector space of interpolating polynomials.…
Atman Vachhani, Mathematics IT, Today’s safe computing practices
This Wednesday, April 10th, from 11AM-12PM in SAS Hall room 4201, Atman Vachhani from Mathematics IT will be leading an interactive seminar on today's safe computing practices. You'll have the opportunity to walk through some basic, and some not so basic ways to make sure you and your data stay safe on the open web. Regardless…
Chris Scaduto, Simons Center for Geometry & Physics, Instantons and lattices of smooth 4-manifolds with boundary
Given a 3-manifold Y, what are the possible definite intersection forms of smooth 4-manifolds with boundary Y? Donaldson's theorem says that if Y is the 3-sphere, then all such intersection forms are standard integer Euclidean lattices. I will survey some new progress on this problem, for other 3-manifolds, that comes from instanton Floer theory.
Wen Shen, Penn State University, Scalar Conservation Laws with Discontinuous and Regulated Flux
SAS 4201Conservation laws with discontinuous flux functions arise in various models. In this talk we consider solutions to a class of conservation laws with discontinuous flux, where the flux function is discontinuous in both time and space, but regulated in the two variables. Convergence and the uniqueness of the vanishing viscosity limit for the viscous equation…
Anila Yadavalli, NC State, A curvy way to send messages
SAS 2102Need a more private way of sending notes to your friends during class? Elliptic Curve Cryptography is a method of sending secure messages using tools from algebra and geometry. In this talk, I will introduce some of the ideas behind this encryption scheme originally introduced by Diffie and Hellman. This talk will be accessible to…
Tea and Cookies
SAS 4104Sergey Fomin, University of Michigan, Morsifications and Mutations
SAS 1102I will discuss a new and somewhat mysterious connection between singularity theory and cluster algebras, more specifically between the topology of isolated singularities of plane curves and the mutation equivalence of quivers associated with their morsifications. The talk will assume no prior knowledge of any of these topics. This is joint work with Pavlo Pylyavskyy,…
Juan Villarreal, Virginia Commonwealth University, Logarithmic singularities in vertex algebras
In this talk we want to consider a different kind of singularities in logarithmic vertex algebras. In vertex algebras many properties arise from the locality of their fields. In particular, this implies the expansion of their brackets into a base of delta function and its derivatives. On the other hand some examples in physics lead us to consider some non-local…
Pierre Degond, Imperial College, London, Mathematical models of collective dynamics and self-organization
In this talk, I will review some mathematical challenges posed by the modeling of collective dynamics and self-organization. Then, I will focus on two specific problems, first, the derivation of fluid equations from particle dynamics of collective motion and second, the study of phase transitions and the stability of the associated equilibria.
Jacek Brodzki, Centre for Geometry, Topology, and Applications, Southampton, Persistence in action: quantifying the topology of lungs
Cox 306Topology is dedicated to the study of shapes, and its starting point is an easy-sounding question: How can I tell if two objects are similar? While humans are very adept at distinguishing a large variety of shapes, it is not always easy to say precisely what makes this object similar to or distinct from that…
Aida Maraj, University of Kentucky, Quantitative Properties of Ideals arising from Hierarchical Models
SAS 4201We will discuss hierarchical models and certain toric ideals as a way of studying these objects in algebraic statistics. Some algebraic properties of these ideals will be described and a formula for the Krull dimension of the corresponding toric rings will be presented. One goal is to study the invariance properties of families of ideals…
Jen Hom, Georgia Tech, Heegaard Floer and homology cobordism
We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains an infinite-rank subgroup and a Z-summand. The proof relies on the involutive Heegaard Floer homology package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is joint work with I. Dai, M. Stoffregen, and L. Truong.
Peter Wolenski, Louisiana State University, Fully convex Bolza problems with state constraints and impulses
SAS 4201In this talk, we shall review the Hamilton-Jacobi theory for A Fully Convex Bolza (FCB) problems when the data has no implicit state constraints and is coercive, in which case the minimizing class of arcs are Absolutely Continuous (AC).
Boris Mordukhovich, Wayne State University, Criticality of Lagrange Multipliers in Conic Programming with Applications to Superlinear Convergence of SQP
SAS 4201His talk concerns the study of criticality of Lagrange multipliers in variational systems that have been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments dealing with polyhedral KKT systems and the like, we now focus on general nonpolyhedral systems that are associated, in particular, with…
Retirement Reception for Dr. Griggs
SAS 4104Aram Dermenjian, University of Quebec at Montreal, Facial weak order in hyperplane arrangements
We discuss the facial weak order, a poset structure that extends the poset of regions on a central hyperplane arrangement to the set of all faces of the arrangement which was first introduced on the braid arrangements by Krob, Latapy, Novelli, Phan and Schwer. We provide various characterizations of this poset including a global one, a local one, one using…