This article is devoted to a general class of one dimensional NLS problems with a cubic nonlinearity. The question of obtaining scattering, global in time solutions for such problems has…
Classically, the primary objects one was concerned with in algebraic geometry were the zero sets of systems of polynomial functions, which we call varieties. Since the work of Grothendieck, the…
Of primary importance in computational science and applications is quantification and improvement of predictive capabilities of large-scale parameterized models, which often require the use of multi-query techniques that are intractable for…
The Morrey Conjecture concerns quasi-convexity and rank-one convexity of functions. While the former implies the latter, it's unclear if the converse is true. Sverak proved the conjecture in 3D, but…
Disorder is a fact of life, and controlling it on the nanoscale is complex, expensive, and of limited use. On the other hand, disordered materials do offer a range of…
Fusion categories are algebraic gadgets that have seen many applications in topology and mathematical physics. In particular, they can be used to encode topological quantum field theories in the sense…
Motivated by motion of myxobacteria, we review several kinetic approaches for modeling motion of self-propelled, interacting rods. We will focus on collisional models of Boltzmann type and discuss the derivation…
SAS 4201 (Zoom link: https://ncsu.zoom.us/j/93542716306?pwd=c1Iyc0s2bUJhWUR0R2ZNcmlLSHJqQT09)
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…