Let Σ be a closed surface (i.e. a 2-dimensional Riemannian manifold) satisfying the following condition: the first eigenvalue of the elliptic operator -Δ+βK is nonnegative, where K is the Gauss curvature and β is a positive constant . This condition was mainly motivated by the studies of positive scalar curvature in dimension three, and soon…
Given a modular category C, the irreducible characters of its fusion ring are in one-to-one correspondence with the set Irr(C) of isomorphism classes of simple objects of C. Consequently, the action of the absolute Galois group on these characters induces a permutation action on Irr(C). The analysis of this action is essential to the classification…
his talk presents various characterizations of the subdifferential of the pointwise supremum of an arbitrary family of convex functions, as well as some featured applications. Starting by the maximum generality framework, we move after to particular contexts in which some continuity and compacity assumptions are either imposed or inforced via processes of compactification of the…
The learning session will focus on the general operations of the Office of Student Conduct. The presenter will discuss the key procedures associated with academic misconduct cases, including proper adjudication techniques for faculty and how to properly report cases to OSC. The presenter will also provide best practices for promoting academic integrity in courses and how to…
In linear algebra we know that the Pfaffian of an antisymmetric matrix is a square root of the determinant of matrix. In this talk I will explain how one does the quantum linear algebra, a recent popular area that can be traced back to Gauss and is well connected with many areas of mathematics such as…
Computing the homology of semialgebraic sets is a central problem in computational real algebraic geometry. However, as of today, all symbolic algorithms for this problem require still time that is doubly exponential with respect to the number of variables. The latter is so although the size of the Betti numbers is known to be singly…
Data or patterns (e.g., signals and images) emanating from physical sensors often exhibit complicated nonlinear structures in high dimensional spaces, which post challenges in constructing effective models and interpretable machine learning algorithms. When data is generated through deformations of certain templates, transport transforms often linearize data clusters which are non-linear in the original domain. We…
In this talk I will show that the Morse index of the critical Moebius band in the 4-dimensional Euclidean ball equals 5. This result makes use of the quartic Hopf differential technique and a comparison theorem between the index of a free boundary minimal surface in the Euclidean ball and its spectral index. The latter also enables us to reprove…
Speaker’s webpage: http://sinanaksoy.com/ Location: Jointly in person and virtually on Zoom. SAS 2225 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at cmjones6@ncsu.edu to be added.
This presentation will feature some hands on activities for thinking about getting ready for job interviews, both inside and outside academia.
Room: SAS 2235 Zoom Meeting link: https://ncsu.zoom.us/j/95923219557?pwd=T3MzUEZRazRaY2tBdjl1dFVJOG50QT09
Suppose we observe very few entries from a large matrix. Can we predict the missing entries, say assuming the matrix is (approximately) low rank ? We describe a very simple method to solve this matrix completion problem. We show our method is able to recover matrices from very few entries and/or with ill conditioned matrices,…
Talk 1: Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling - Abstract 1: Sensitivity analysis for computational fluid dynamics (CFD) simulations is a complicated procedure, which still relies, in many cases, on engineering judgment and factors of safety. This is, in part, because the computational cost of quantifying the simulation's sensitivity to all…
Tensor method can be used for compressing high-dimensional functions arising from partial differential equations (PDE). In this talk, we focus on using these methods for the simulation of transition processes between metastable states in chemistry applications, for example in molecular dynamics. To this end, we also propose a novel generative modeling procedure using tensor-network without…
In this talk, we will survey G2-structures, which are cross product structures on 7-manifolds, and we will discuss recent developments on a natural geometric flow of G2-structures called Laplacian flow. The Laplacian flow was introduced by Robert Bryant as a tool to explore the geometry of G2-structures on 7-manifolds and to construct examples of G2-holonomy…
Since Chuang and Rouquier's pioneering work showing that categorical sl(2)-actions give rise to derived equivalences, the construction of derived equivalences has been one of the more prominent tools coming from higher representation theory. In this talk, we explain joint work with Aaron Lauda and Laurent Vera giving new super analogues of these derived equivalences stemming…
DELTA staff will share about a course design framework and instructional tools for blended/flipped teaching and learning, as well as other teaching resources. Supported by literature in instructional design and educational psychology, the framework has been applied and improved through DELTA Grant course design projects over the past eight years, including two math courses (MA…
INVITATION TO MATHEMATICS GRADUATION CEREMONY Friday, December 16, 2022, 12:30 pm 2203 SAS Hall ~ A reception will follow the ceremony ~ Please save the date for the Department of Mathematics Fall 2022 Graduation Ceremony. Join us to celebrate the students that have earned a degree in Mathematics for Fall 2022.
The stochastic processes of evolution have generated DNA, RNA, and protein sequences. These sequences determine how these entities chemically interact with themselves and each other, form physical structures, and functionally behave as signals and/or machines within cells. My research involves reconstructing the history of the stochastic processes that led to the sequences we observe today…
We define vertex-colourings for edge-coloured digraphs, which unify the theory of P-partitions and proper vertex-colourings of graphs. Furthermore, we use our vertex-colourings to define generalized chromatic functions, which merge the chromatic symmetric and quasisymmetric functions and generating functions of P-partitions. We also discuss the relations between generalized chromatic functions, Schur functions in noncommuting variables, and the well-known Stanley-Stembridge (3+1)-free conjecture.