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Asymptotics for solubility of unit equations over real quadratic fields

For a real quadratic field K and positive integer r, we prove an asymptotic formula for the number of rational integers of bounded absolute value that can be written as a sum of r units of the ring of...

The Gamma disordered Aztec diamond

The Aztec diamond, under the uniform measure on domino tilings, is one of the classic examples of an exactly solvable model in probability and statistical mechanics. Its rich geometric features—such a...

Some tricks to deal with group actions in positive characteristic.

Through a series of examples (all involving at most $3\times 3$ matrices, as with bigger groups it is clearly impossible to do a correct computation on the board), we illustrate some of the pathologie...

Central limit theorems for sequential systems

The fluctuations of Birkhoff averages for strongly chaotic systems are well known to satisfy a Central Limit Theorem. However, many systems of interest are non-autonomous, prompting the question ...

Bimeromorphic Properties of Locally Conformally Kähler Manifolds

I shall give a brief introduction in LCK geometry, then focus on the existence of a minimal model for a certain subclass. If time permits, I shall discuss other bimeromorphic properties too....

The role of the curvature in the uniqueness of the critical point of solutions to elliptic PDEs

We consider positive, semi-stable solutions of −Delta u = f(u) on domains of the model spaces of constant curvature. We provide geometric conditions on the domains guaranteeing the uniqueness and the ...

Wave function renormalization in particle-field models

Operator-theoretic renormalization of particle-field models is typically done by subtracting diverging contributions to the Hamiltonian. In many interesting  cases, however, an additional wave fu...

Ornstein—Zernike theory for the near-critical planar random cluster model

In this talk, we will discuss the classical Ornstein-Zernike theory for the random-cluster model (also known as FK percolation). In its modern form, it is a very robust theory, which most celebrated o...

La teoria di De Giorgi–Nash–Moser per le equazioni cinetiche con diffusione non locale

Sunto: Presenterò alcuni risultati recenti riguardanti le soluzioni deboli di un'ampia classe di equazioni integrali cinetiche, in cui il termine di diffusione nella variabile di velocità è un operato...

High Order Structure-Preserving Semi-Implicit Schemes for Hyperbolic Equations

Programma: 9:30-10:20 Sergio Pirozzoli: TBACoffee Break11:00-11:30 Tommaso Tenna: From the multi-species Boltzmann equation to an isentropic two-phase flow model: kinetic derivation and numerical insi...