In calculus, we study series and learn how to add infinitely many numbers--but how about multiplying infinitely many numbers? In this talk, we'll start with familiar series from calculus, and then move on to study more exotic infinite sums and infinite products and the interactions between them. We'll see some number theory, complex analysis, and…
An important construction for (the information theoretic version of) semantic security is a "Biregular Irreducible Function" (BRI). These can be constructed from a complete biregular graph on $2^k d \times 2^k d$ by by coloring it with $2^k$ colors in such a way that each vertex has degree $d$ in each color. Good BRI's are…
Upcoming meeting: Saturday, March 30, 2019 Location: Wake Forest University in Winston-Salem, NC Lecture Hall: Manchester 16 More information: https://wp.math.ncsu.edu/tlc/ Speakers: James Haglund, University of Pennsylvania Adam Marcus, Princeton University Jennifer Morse, University of Virginia Nathan Reading, North Carolina State University Registration and funding applications: To register and/or apply for funding, please fill out this form. If you have…
Turn on a light in the middle of a room: Is every spot illuminated? If the room is a complicated labyrinth, then probably not, but what if the walls of the room are mirrors? Amie Wilkinson of the University of Chicago will deliver the Department of Mathematics Kwangil Koh Lecture on Mathematics in Our Time through…
The incompressible Euler equation of fluid mechanics describes motion of ideal fluid, and was derived in 1755. In two dimensions, global regularity of solutions is known, and double exponential in time upper bound on growth of the derivatives of solution goes back to 1930s. I will describe a construction of example showing sharpness of this…
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,…