The age of AI requires building capable and more efficient neural networks that are mainly achieved via (I) Developing and manufacturing more capable hardware; (II) Designing smaller and more robu...
The celebrated Osterwalder-Schrader (OS) reconstruction results provide conditions verified by Euclidean n-point correlation functions to produce a Wightman quantum field theory. This talk aims to sho...
In the past few decades the fractional Laplacian (−∆)s has capitalized the attention of the PDE community as an integrodifferential operator which is the nonlocal counterpart to the classical Laplacia...
Games, voting, networks, and numerous other topics have been explored by both mathematicians and economists, each employing their own language, methodologies, and theoretical frameworks. The purpose o...
Different interplays between different fields of Mathematics and different domains of Social Sciences The need for quantitative predictions in Social Sciences has very much increased in the last de...
We will prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we will obtain a new proo...
The intersection theory of the moduli space of stable curves is one of the central topics of enumerative geometry, a subject with connections to Gromov-Witten theory, integrable systems, and complex g...
In recent years there has been a growing interest in Ramsey theory and related problems in combinatorics of numbers. Historically, the earliest results in this field are Schur's Theorem ("In every fin...
For a framed n-manifold M one can produce an explicit pairing between M and its one point point compactification M^+, taking values in S^n, which on homology induces the Poincaré duality pairing. We s...
Isogeny theorems are a powerful number-theoretic tool to understand subgroup of elliptic curves over number fields and through those, properties of their rational points. As a prerequisite for such th...