| 27/05/21 | Seminario | 14:00 | 15:00 | | Costante Bellettini | University College London (UK) | Seminario di Equazioni Differenziali
Existence of hypersurfaces with prescribed-mean-curvature
(MS Teams link for the streaming at the end of the abstract)
Let N be a compact Riemannian manifold of dimension 3 or higher, and g a Lipschitz non-negative (or non-positive) function on N. We prove that there exists a closed hypersurface M whose mean curvature attains the values prescribed by g (joint work with Neshan Wickramasekera, Cambridge). Except possibly for a small singular set (of codimension 7 or higher), the hypersurface M is C^2 immersed and two-sided (it admits a global unit normal); the scalar mean curvature at x is g(x) with respect to a global choice of unit normal. More precisely, the immersion is a quasi-embedding, namely the only non-embedded points are caused by tangential self-intersections: around such a non-embedded point, the local structure is given by two disks, lying on one side of each other, and intersecting tangentially (as in the case of two spherical caps touching at a point). A special case of PMC (prescribed-mean-curvature) hypersurfaces is obtained when g is a constant, in which the above result gives a CMC (constant-mean-curvature) hypersurface for any prescribed value of the mean curvature.
The construction of M is carried out largely by means of PDE principles: (i) a minmax for an Allen--Cahn (or Modica-Mortola) energy, involving a parameter that, when sent to 0, leads to an interface from which the desired PMC hypersurface is extracted; (ii) quasi-linear elliptic PDE and geometric-measure-theory arguments, to obtain regularity conclusions for said interface; (iii) parabolic semi-linear PDE (together with specific features of the Allen-Cahn framework), to tackle cancellation phenomena that can happen when sending to 0 the Allen-Cahn parameter.
Link
Note: Sponsored by the Grant MATH@TOV |
| 26/05/21 | Seminario | 16:00 | 17:00 | | Fabio Cipriani | (Politecnico Milano) |
Densities and their measurability in NCG
- online seminar - link to MS teams in the abstract
Abstract: The aim of the talk is to provide conditions ensuring Connes' measurability
of the canonical, $(1,infty)$-summable, spectral weight
$ho(D)$, we associate
to any self-adjoint operator $D$ with discrete spectrum and of its associated state $phi_D(T):={
m Tr,}_omega (T
ho(D))$. The framework allows to discuss measurability for discrete groups with sub-exponential growth and $ heta$-summable spectral triples. Examples also include 1. the volume density of Euclidean domains of infinite volume 2. densities on the C$^*$-algebra of pseudo-differential operators of 0-order on a compact Riemannian manifold 3. densities on Toeplitz extensions.
This talk is part of the activity of the MIUR Excellence Department
Project MATH@TOV CUP E83C18000100006.
Link MS Teams
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| 21/05/21 | Seminario | 15:00 | 16:00 | | Sachin GAUTAM | Ohio State University |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"R-matrices and Yangians"
- in streaming mode -
(see the instructions in the abstract)
An R-matrix is a solution to the Yang-Baxter equation (YBE), a central object in Statistical Mechanics, discovered in 1970's. The R-matrix also features prominently in the theory of quantum groups formulated in the eighties. In recent years, many areas of mathematics and physics have found methods to construct R-matrices and solve the associated integrable system.
In this talk I will present one such method, which produces meromorphic solutions to (YBE) starting from the representation theory of a family of quantum groups called Yangians. Our techniques give (i) a constructive proof of the existence of the universal R-matrix of Yangians, which was obtained via cohomological methods by Drinfeld in 1983, and (ii) prove that Drinfeld's universal R-matrix is analytically well behaved.
This talk is based on joint works with Valerio Toledano Laredo and Curtis Wendlandt.
N.B.: please click HERE to attend the talk in streaming
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| 20/05/21 | Seminario | 16:00 | 17:00 | | Umberto Zannier | Scuola Normale Superiore di Pisa |
DinAmicI: Another Internet Seminar (DAI Seminar)
”Torsion values of sections, elliptical billiards and
diophantine problems in dynamics”
- in streaming mode -
(see the instructions in the abstract)
After a very brief review of basics on elliptic curves and their families, we shall consider "sections" of such families, and especially their "torsion values". For instance, what can be said of the complex numbers b for which (2, sqrt{2(2-b)}) is torsion on the Legendre curve y^2=x(x-1)(x-b)? In particular, we shall recall results of "Manin-Mumford type" and focus to illustrate some applications to elliptical billiards. Finally, if time allows we shall frame these issues as special cases of a general question in arithmetic dynamics, which can be treated with different methods, depending on the context. (Most results refer to work with Pietro Corvaja and David Masser.)
Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
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| 20/05/21 | Seminario | 14:30 | 17:50 | Aula Gismondi | | | Workshop "Entropy and QFT"
h. 14:30 - 15:15 Daniela Cadamuro (University of Leipzig)
Relative entropy of coherent states on general CCR algebras
h. 15:30 - 16:15 Rainer Verch(University of Leipzig)
Temperature and entropy-area relation of quantum matter near spherically symmetric outer trapping horizons
h. 16:30-16:50 Tea break
h. 16:50 - 17:35 Marius Junge (University of Illinois)
Poissonization, boundary and relative entropy
- in streaming mode - conference
registration required.
NB:This workshop is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
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| 20/05/21 | Seminario | 14:00 | 15:00 | | Giovanni Molica Bisci | Università degli Studi di Urbino | Nonsmooth functionals in the Calculus of Variations
( MS Teams Link for the streaming )
Link to the abstract
NB: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 19/05/21 | Seminario | 14:00 | 18:15 | | | | Workshop "Entropy and QFT"
h. 14:00 -14:10 Welcome
h. 14:10 - 14:55 Stefan Hollands (University of Leipzig)
State recovery
h. 15:10 - 15:55 Chris J. Fewster(University of York)
Quantum Energy Inequalities
h. 16:10-16:30 Tea break
h. 16:30 - 17:15 Thomas Faulkner (University of Illinois)
Some new results on reflected entropy
h. 17:30 - 18:15 Feng Xu (University of California, Riverside) Rigorous results about Relative entropy in QFT
- in streaming mode - conference
registration required.
NB:This workshop is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
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| 14/05/21 | Colloquium | 15:00 | 17:00 | | Maria Colombo | Swiss Federal Institute of Technology (Lausanne) | May 12: Celebrating Women in Mathematics in Rome
The Transport equation
(With an opening address by Roberta Fulci)
For more information about this event visit this
webpage (which contains also the link for the streaming of the event).
This is part of the international initiative
May 12: Celebrating women in Mathematics
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 |
| 13/05/21 | Seminario | 14:00 | 15:00 | | Simone Secchi | Università di Milano Bicocca | Concentration phenomena for the Schroedinger-Poisson system in R^2
( MS Teams Link for the streaming )
We present some recent results obtain in collaboration with Denis Bonheure (Bruxelles, Belgium) and Silvia Cingolani (Bari, Italy) about a semiclassical analysis for a planar Schroedinger-Poisson system with potential functions.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
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| 12/05/21 | Seminario | 16:00 | 17:00 | | Jacopo Bassi | Univ. Tor Vergata |
Amenability properties for SL(3,Z)
in streaming mode - link in the abstract
Motivated by analogies with the case of SL(2,Z), we introduce a method for the study of possible variants of the Akemann-Ostrand property for SL(3,Z). This is a joint work in progress with Florin Radulescu.
This talk is part of the activity of the MIUR Excellence Department
Project MATH@TOV CUP E83C18000100006.
MS Teams link
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