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Nonlinear potential theory and elliptic regularity theory are two classical topics in the modern analysis of partial differential equations. In this talk I show how these themes merge to solve the lon...
I will start by reviewing an old joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten, Gopakumar-Vafa and stable pair invariants on compact Calabi-Yau 4-folds. For non-compact CY4...
The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a ...
Consider a point mass falling vertically on an infinitely heavy horizontal plate which oscillates periodically with period 2π in the vertical direction and interacts with the particle by the l...
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution o...
In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities for positive solutions of backward hea...
It is believed that the N400 elicited by concepts belonging to Living is larger than N400 to Objects. This is considered as evidence that concepts are organized, in the brain, on the basis of categori...
The characterisation of seismic sources with timereversed wave fields is developing into a standard technique that has already been successful in numerous applications.
The incidence of diabetes mellitus and cardiovascular diseases is increasing at a worrisome rate globally. Diabetes mellitus is known to occur due to high blood glucose levels, caused by defects in in...
Interactions between food demand, biomass energy and forest preservation are driving both food prices and land-use changes, regionally and globally. This study presents a new model called Nexus Land-U...
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
We study effective potentials coming from compactifications of string theory. We show that, under mild assumptions, such potentials are bounded from below in four dimensions, giving an affirmative ans...
We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schr\"odinger equation in $\R^{N}, N\ge 3$, in presence of a singular external potential.
We prove that the quivers with potentials associated by the author to ideal triangulations of punctured surfaces with empty boundary are non-degenerate, provided the number of punctures is 1 or greate...
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics ...

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