Alex Chandler, NC State, Spectral Sequences Working Seminar
Spectral sequences in Khovanov homology.
Spectral sequences in Khovanov homology.
My research has been in two broad areas namely mathematical biology and disability studies. This talk will touch upon three of my projects in mathematical biology and one project in disability studies. The mathematical biology section will cover the work I have done in investigating permanence (species in a system are at a safe threshold…
The cosmetic surgery conjecture states that no two surgeries on a given knot produce the same 3-manifold (up to orientation preserving diffeomorphism). Floer homology has proved to be a powerful tool for approaching this problem; I will survey partial results that are known and then show that these results can be improved significantly. If a…
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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.…
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…
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.
Conservation 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…
Need 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…
I 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,…
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…
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.
Topology 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…
We 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…
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.
In 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).
His 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…