## Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma

Settimana dal 01-04-2019 al 07-04-2019

Lunedì 01 aprile 2019
Ore 10:30, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Corso di Dottorato
Fabio Lucio Toninelli (Università di Lyon 1)
The dimer model: equilibrium and non-equilibrium aspects
This course focuses on various mathematical aspects of lattice dimer models. These are very classical two-dimensional statistical mechanics models, that are exactly solvable in some sense (Kasteleyn, 1961): partition function and correlations can be computed in determinantal form. Recently there has been a new wave of interest in dimer models, both in probability, combinatorics and mathematical physics. One reason is that these models, as well as other two-dimensional critical models, exhibit conformal invariance properties. Another interesting aspect is that they allow to obtain very nice Markov dynamics of two-dimensional interfaces, whose large-scale dynamical behavior can be studied. Detailed contents:

• Kasteleyn theory (partition functions, correlations, determinantal properties)
• correlations and representation determinantale
• thermodynamic limit and ergodic Gibbs measures
• height fluctuations and massless Gaussian field
• dynamics of dimer models: mixing time and hydrodynamic limits.
References :
• R. Kenyon, Lectures on dimers, arXiv:0910.3129.
• F. Toninelli, Lecture notes on the dimer model, http://math.univ-lyon1.fr/homes-www/toninelli/noteDimeri.pdf

Lunedì 01 aprile 2019
Ore 14:15, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
The Restriction of the Fourier Transform to Surfaces: the Hyperbolic Case
The problem of restriction of the Fourier transform to hypersurfaces (or more generally to submanifolds in $$\mathbb{R}^n$$) was posed by Stein in the seventies. This operator, in its adjoint form, is a powerful tool in the study of dispersive equations. Also, the restriction operator can be thought as a model case for more complicated oscillatory integral operators, for instance, the spherical summation operators. We will make a review of this problem, which is still open. We will present some new results for the case of surfaces with negative curvature.

Lunedì 01 aprile 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Algebra and Representation Theory Seminar
Dmitriy Rumynin (University of Warwick)
Kac-Moody Groups: representations, localisation, duality
We will look at representation theory of a complete Kac-Moody group G over a finite field. G is a locally compact totally disconnected group, similar, yet slightly different to the group of points of a reductive group scheme over a local field. After defining the group we will prove that the category of smooth representations has finite homological dimension. At the end we discuss localisation and homological duality for this category. N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

Lunedì 01 aprile 2019
Ore 16:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario
Claudio Landim (IMPA, Rio de Janeiro, Brazil)
Homogenization for diffusion processes, part 3
Homogenization od diffusion processes in stationary random environment. Characterizations of the homogenizaed diffusion coefficient.

Mercoledì 03 aprile 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Maria Gorelik (The Weizmann Institute of Science (Israel))
Snowflake modules for Lie superalgebras
Quasi-integrable modules over symmetrizable Kac-Moody algebras form a semisimple subcategory in the category O. For affine Lie algebras these modules appear as modules over a simple vertex algebra (Arakawa's Theorem). In this talk I will speak about a joint project with V. Serganova studying quasi-integrable (snowflake) modules for Lie superalgebras.

Mercoledì 03 aprile 2019
Ore 14:30, Aula 1B1, Dipartimento di Scienze di Base ed Applicate per L'Ingegneria
Analisi MaTÉmatica allo SBAI
Azahara DelaTorre (Albert-Ludwigs-Universität Freiburg)
Concentration phenomena for the fractional $$Q$$-curvature equation in dimension 3 and fractional Poisson formulas
We study the compactness properties of metrics of prescribed fractional $$Q$$-curvature of order 3 in $$\mathbb{R}^3$$. We will use an approach inspired from conformal geometry, seeing a metric on a subset of $$\mathbb{R}^3$$ as the restriction of a metric on $$\mathbb{R}^4_+$$ with vanishing fourth-order $$Q$$-curvature. In particular, we will show that a sequence of such metrics with uniformly bounded fractional $$Q$$-curvature can blow up on a large set (roughly, the zero set of the trace of a nonpositive biharmonic function $$\Phi$$ in $$\mathbb{R}^4_+$$, in analogy with a $$4$$-dimensional result of Adimurthi-Robert-Struwe, and construct examples of such behaviour. In doing so, we produce general Poisson-type representation formulas (also for higher dimension), which are of independent interest. This is a work done in collaboration with María del Mar González, Ali Hyder and Luca Martinazzi.

Mercoledì 03 aprile 2019
Ore 15:30, Aula 1B1, Dipartimento di Scienze diBase ed Applicate per l'Ingegneria
Analisi MaTÉmatica allo SBAI
Luca Battaglia (Università di Roma Tre)
A double mean field approach for a curvature prescription problem
I will consider a double mean field-type Liouville PDE on a compact surface with boundary, with a nonlinear Neumann condition. This equation is related to the problem of prescribing both the Gaussian curvature and the geodesic curvature on the boundary. I will discuss blow-up analysis, a sharp Moser-Trudinger inequality for the energy functional, existence of minmax solution when the energy functional is not coercive. The talk is based on a work in progress with Rafael Lopez-Soriano (Universitat de Valencia).

Venerdì 05 aprile 2019
Ore 12:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario MoMA
Anton Bovier (Università di Bonn )
Stochastic individual based models: from scaling limits to modelling of cancer therapies
Stochastic individual base models, that is, measure valued Markov processes describing the evolution of interacting biological populations, have proven over the last years to be effective models in deriving key features of the theory of adaptive dynamics, such as the canonical equation of adaptive dynamics, the trait substitution sequence and the polymorphic evolution sequence. In this talk I review these models an the diverse emerging scaling limits, and I report on recent progress in applying such models to the modelling of cancer therapies, and in particular to immunotherapy and combination therapies of melanoma, based on experimental data by colleagues from the Bonn university hospital.

Venerdì 05 aprile 2019
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario per Insegnanti (Piano Lauree Scientifiche)
Francesca Tovena*, Giuseppe Casale**, Davide Passaro** (*Università di Tor Vergata, **Liceo Russell)
Esperienze di coding per il liceo matematico

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