相关论文: The Soap Bubble Theorem and Serrin's problem: quan…
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
This is the introductory part of my Ph.D thesis, defended at the Faculty of Science and Technology, NTNU on December 10, 2012.
We show, using the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim, that the statistics of the current of the symmetric simple exclusion process (SSEP) connected to two reservoirs are the same on an…
This is my Ph.D. thesis written under the direction of Prof. Joseph Bernstein at Tel-Aviv University. Submitted: March 2005.
In this note we consider a question related to the high-dimensional generalization of the classical Severi's finiteness theorem for curves. We will introduce some background and then state the main result. The proof of the main result is…
The goal of this PhD thesis is to study a diophantine approximation problem stated by Schmidt in 1967. The problem aim to study the approximation of a subspace of $\mathbb{R}^n$ by rational subspaces, not necessarily of the same dimension,…
Soap bubbles and foams have been extensively studied by scientists, engineers, and mathematicians as models for organisms and materials, with applications ranging from extinguishing fires to mining to baking bread. Here we provide some…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…
Unabridged version of the Thesis presented to the University of L' Aquila, in partial fulfillment of the requirements for the ``Laurea'' degree in Physics, October 1998. Work carried out at the University of L'Aquila and at the University…
We prove integral formulas for closed hypersurfaces in C^{n+1}, which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the…
The persistent decay of bubble clusters in coarsening two-dimensional soap froths is measured experimentally as a function of cluster volume fraction. Dramatically stronger decay is observed in comparison to soap froth models and to…
The paper provides optimal quantitative stability estimates for the celebrated Alexandrov's Soap Bubble Theorem within the class of $C^{k,\alpha}$ domains, for any $k \ge 1$ and $0 < \alpha \leq 1$, by leveraging Gagliardo-Nirenberg-type…
This paper represents an elaboration of the lectures delivered by one of us (CAF) during "Course 197 -- Foundations of Quantum Physics" at the International School of Physics "Enrico Fermi" in Varenna, Italy, July 2016. Much of the material…
This review article discusses recent progress in understanding of various families of integrable models in terms of algebraic geometry, representation theory, and physics. In particular, we address the connections between soluble many-body…
Soap bubbles are thin liquid films enclosing a fixed volume of air. Since the surface tension is typically assumed to be the only responsible for conforming the soap bubble shape, the realized bubble surfaces are always minimal area ones.…
In this talk I discuss some recent developments in physics beyond the Standard Model. After some initial comments on neutrino masses, I discuss the status of low-energy supersymmetry and finally turn to describing some recent work in…
I give a general non-technical review of supersymmetry and its modern applications in phenomenology and quantum field theories at strong coupling. Invited Talk at the conference {\sl Frontiers of Fundamental Physics, FFP16, May 23-26, 2022,…
We prove a quantitative version of the Polynomial Szemeredi Theorem for difference sets. This result is achieved by first establishing a higher dimensional analogue of a theorem of Sarkozy (the simplest non-trivial case of the Polynomial…
This is is a copy of dissertation that I have submitted in defense of my ph.d. thesis, with some minor changes that I have made since then. The goal of the project is to generalize matter fields and their Lagrangians from regular space time…
We discuss the application of the AdS/CFT correspondence to possibly gain new physical insights for the strongly coupled quark-gluon plasma. This article provides an informal summary of a talk given by RCM at the 18th International…