Hypertoric varieties are quaternionic analogs of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and hyperkahler geometry. In the last decade, hypertoric varieties have appeared prominently in investigations of symplectic duality, a mathematical incarnation of 3d mirror…
The classical Descartes’ rule of signs provides an easily computable upper bound for the number of positive real roots of a univariate polynomial with real coefficients. Descartes' rule of signs is of special importance in applications where positive solutions to polynomial systems are the object of study. This is the case in reaction network theory…
Deep neural networks (DNNs) have gained undeniable success as high-dimensional function approximators in countless applications. However, there is a significant hidden cost behind triumphs - the cost of training. Typically, DNN training is posed as a stochastic optimization problem with respect to the learnable DNN weights. With millions of weights, a non-convex and non-smooth objective…
The Z-hat invariant, proposed by Gukov, Pei, Putrov, and Vafa, is a fascinating q-series invariant of three-manifolds related to various areas of mathematics and physics. We want to find a topological quantum field theory (TQFT) that computes this invariant to understand it better. This invariant cannot come from TQFT in the sense of Atiyah, as…
We are concerned with the rigorous justification of the so-called hard congestion limit from a compressible system with singular pressure towards a mixed compressible-incompressible system modeling partially congested dynamics, in the framework of BV solutions. We will consider small BV perturbations of reference solutions constituted by (possibly interacting) large interfaces, and we will analyze the dynamics of…
Please SAVE THE DATE for the Department's Awards Ceremony and End of Semester Meeting. ceremony and tea to follow.
Deep learning is one of the most universal techniques in the modern big data era, achieving remarkable success across imaging, healthcare, natural language processing, and more. As applications begin to rely more heavily on deep learning, it is crucial that we understand how these algorithms make predictions and how we can make them better (e.g.,…
Once per semester, the Teaching and Learning Seminar will host 10-minute "lightning talks" in which 4 graduate students and/or faculty members will talk about some element of their teaching that they'd like to share. This may be a cool example you came up with for a class you are teaching, an innovative teaching technique or…
Please save the date for the College of Sciences’ annual Faculty and Staff meeting at 4 p.m. on Wednesday, April 20, in 301 Riddick Hall. Interim Dean John Blondin will join us as we discuss topics that are important to you. There will be time for you to ask questions too.A reception in the Riddick Hearth…
Deep learning is one of the most universal techniques in the modern big data era, achieving remarkable success across imaging, healthcare, natural language processing, and more. As applications begin to rely more heavily on deep learning, it is crucial that we understand how these algorithms make predictions and how we can make them better (e.g.,…
Symmetric functions are very interesting combinatorial objects. After decomposing certain symmetric functions in terms of different bases, we can often combinatorially interpret the resulting coefficients. This is made particularly easy if those coefficients are positive (or controllably negative). The chromatic symmetric function is one such symmetric function, and its decomposition has been of interest for…
Congenital heart disease affects 1 in 100 infants and is the leading cause of infant mortality in the US. Among the most severe forms of congenital heart disease is single ventricle physiology, in which the heart develops with only one functional pumping chamber. These patients typically undergo three open chest surgeries, culminating in the Fontan…
Many areas of interest within the Earth are anisotropic, meaning that the speed of sound is different in different directions. It turns out that pressure waves are far better behaved than shear waves, but fortunately the different polarizations are coupled together through algebraic geometry. I will explain the surprising power of algebraic geometry in the…
Please join us in person or virtually as we honor our 2023 College of Sciences Awards for Excellence Nominees and winners.
Variational quantum algorithms use non-convex optimization methods to find the optimal parameters for a parametrized quantum circuit in order to solve a computational problem. The choice of the circuit ansatz, which consists of parameterized gates, is crucial to the success of these algorithms. Here, we propose a gate which fully parameterizes the special unitary group…
This article is about yield farming, which refers to a decentralized finance strategy of providing liquidity and seeking associated rewards in the form of transpired-transaction fees. We explain and demystify yield farming and quantify transaction costs, returns, and risks using on-chain data from major decentralized exchanges. We provide a mathematical framework that resembles a representative…
Grade Level(s): High School GIRLS Date(s): Saturday, April 29, 2023 (11:00 am - 2:00 pm) Location: NC State University - SAS Hall Cost: FREE (Capped at 40 students) Description: Discover the beauty of mathematics and its wide applicability and power in everyday life! Why Should I Study Math? What Can I Do with a Math Degree? What Do Mathematicians…
Arvind Saibaba, contact for zoom access.
You are invited to participate in the Mathematics Graduation Ceremony to celebrate the students who completed their mathematics degree in Spring and Summer 2023. Graduation Ceremony will be held on May 5, 2023 at 6pm in McKimmon room 2. Reception to follow the ceremony.
The natural question is: do structures satisfying given open relations (called the genuine solutions of the differential relation) exist on a given manifold? Replacing all derivatives appearing in a differential relation by the additional independent variables one obtains an open subset of the corresponding jet bundle. A formal solution of the differential relation is a…