| 01/04/26 | Colloquium | 16:00 | 17:00 | 1201 Dal Passo | Mikael Rørdam | University of Copenhagen |
Colloquium "Levi-Civita"
The Connes Embedding Problem, Kirchberg’s reformulations, Tsirelson’s conjecture, and MIP*=RE
In his seminal classification paper from 1976, Connes remarked that every separable tracial von Neumann algebra ought to be embeddable into an ultrapower of the hyperfinite type II_1 factor, or, in other words, be approximable by matrices. Over the following decades, the Connes Embedding Problem (CEP) remained unsolved, but many interesting and deep reformulations were discovered. Prominently, Kirchberg proved in his famous 1991 Inventiones paper that CEP is equivalent to several questions concerning C*-algebras and their tensor product, including his QWEP conjecture. He also showed that CEP holds if and only if there is a unique C*-norm of the tensor product of two copies of the full group C*-algebra of the free group. The latter was shown (by several authors) to be equivalent to Tsirelson’s conjecture about quantum correlations. CEP also relates to the open problems in group theory if all infinite discrete groups are sofic. Recently, Ji-Natarajan-Vidick-Wright-Yuen announced a negative solution to Tsirelson’s conjecture, and hence also a negative answer to CEP by proving that two complexity classes are the same |
| 06/03/26 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Thomas WILLWACHER | ETH Zürich |
Algebra & Representation Theory Seminar (ARTS)
"The triconnected Kontsevich graph complex"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
Many objects of interest in algebraic topology can be computed by graph complexes. This includes homotopy groups of embedding spaces and diffeomorphism groups, and in particular (parts of) the cohomology of the moduli space of curves. Unfortunately, the graph homology itself is still a mysterious object and far from being fully understood. In my talk, I will introduce a smaller quasi-isomorphic variant of the most basic graph complex (the commutative graph complex of Kontsevich), and discuss the present state of knowledge of the graph homology. <br>
The talk is based on arXiv:2503.17131 and arXiv:2508.13724.
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<em><small><small> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </small></small></em>
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| 06/03/26 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Azzurra CILIBERTI | Ruhr-Universität Bochum |
Algebra & Representation Theory Seminar (ARTS)
"A multiplication formula for cluster characters in gentle algebras"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
Gentle algebras, introduced by Assem and Skowro?ski, are a well-loved class of algebras. They are string algebras, so their module categories are combinatorially described in terms of strings and bands, they are tiling algebras associated with dissections of surfaces, and they have many other remarkable properties. Furthermore, Jacobian algebras arising from triangulations of unpunctured marked surfaces are gentle.
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In the talk, I will present a multiplication formula for cluster characters induced by generating extensions in a gentle algebra <em>A</em>. This formula generalizes a previous result of Cerulli Irelli, Esposito, Franzen, Reineke. Moreover, in the case where <em>A</em> comes from a triangulation <em>T</em>, it provides a representation-theoretic interpretation of the exchange relations in the cluster algebra with principal coefficients in <em>T</em>.
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<em><small><small> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </small></small></em>
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| 04/03/26 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Stefano Galanda | University of York |
Operator Algebras Seminar
Construction of interacting equilibrium states for
non-relativistic Bose gases with condensation
In this talk I will present a recent construction of
equilibrium states at positive temperature, with and without
Bose-Einstein condensation, for a non-relativistic Bosonic QFT (gas of
Bose particles) in the infinite volume limit, interacting through a
localised two body interaction. In order to obtain this result, we use
methods of quantum field theory in the algebraic formulation and of
quantum statistical mechanics in the operator algebraic setting. The
convergence of the interacting correlation functions is obtained
constructing an equivalent perturbative series expansion introducing an
auxiliary stochastic Gaussian field which mediates the interaction.
Limits where the localisation of the two-body interaction is removed are
eventually discussed in combination with other regimes. This talk is
based on a collaboration with Nicola Pinamonti.
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| 24/02/26 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Lorenzo Brasco | Università di Ferrara | Seminario di Equazioni Differenziali
Eigenvalues of the $p-$Laplacian on general open sets
We start by reviewing the classical spectral theory of the Dirichlet-Laplacian, on a general open set. It is well-known that the spectrum may fail to be purely discrete, in this generality. We then turn our attention to a nonlinear variant of this problem, by considering the case of the $p-$Laplacian with Dirichlet homogeneous conditions. More precisely, we analyze the minmax levels of the constrained $p-$Dirichlet integral: we show that, whenever one of these levels lies below the threshold given by the $L^p$ Poincar\'e constant ''at infinity'', it actually defines an eigenvalue. We also prove a quantitative exponential fall-off at infinity for the relevant eigenfunctions: this can be seen as a generalization of v{S}nol-Simon--type estimates to the nonlinear case.
Some of the results presented have been obtained in collaboration with Luca Briani (TUM Monaco) and Francesca Prinari (Pisa).
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<b>NB</b>:
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This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
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| 24/02/26 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Gianluca Pacienza | Université de Lorraine | Geometry Seminar
Sottovarietà di intersezioni complete di grado alto
È ben noto grazie a un lavoro di Ein del 1988 che le intersezioni complete molto generali di multigrado $(d_1,...,d_c)$ nello spazio proiettivo di dimensione $n$ non contengono curve razionali non appena $d_1+...+d_c geq 2n-c-1 $. Questo risultato è stato reso ottimale ed esteso nel caso delle ipersuperfici grazie a un metodo introdotto da Voisin che ha ispirato lavori ulteriori di Clemens, Ran e miei. Nonostante lavori più recenti di Coskun, Riedl e Yang sempre nel caso delle ipersuperfici, il risultato di Ein è rimasto l’unico disponibile per intersezioni complete di codimensione arbitraria. Nel seminario parlerò di un lavoro in collaborazione con Francesco Bastianelli in cui estendiamo il lavoro di Ein, mescolando l’approccio di Voisin con quello di Coskun, Riedl e Yang.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures |
| 20/02/26 | Seminario | 16:00 | 17:00 | | Georgy SHARYGIN | IHES |
Algebra & Representation Theory Seminar (ARTS)
joint session with the
Topology Seminar
"The symmetries of the full symmetric Toda system and Lie-Bianchi"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
The full symmetric Toda system is a Hamilton system on the space of real symmetric matrices, given by the Lax equation <em>L'</em> = [<em>M</em>(<em>L</em>),<em>L</em>] , where <em>M</em>(<em>L</em>) is the naïve antisymmetrisation of the symmetric matrix <em>L</em> (deleting the diagonal and inverting the sign of the lower-triangular half). This system turns out to be Liouville-integrable and even super-integrable. In my talk I will prove that it satisfies one more integrability criterion, the Lie-Bianchi criterion, based on the study of its symmetries.
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<em><small><small> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </small></small></em>
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| 20/02/26 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Yasushi IKEDA | IHES |
Algebra & Representation Theory Seminar (ARTS)
joint session with the
Topology Seminar
"Argument shift method on algebra U(gl(d))"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)
The argument shift method is a simple but efficient way to produce a commutative subalgebra in a Poisson algebra, in particular in the symmetric algebra of a Lie group. Its main ingredient is an operator on the Poisson algebra that generates the elements of the commutative subalgebra by acting on its center. In my talk I will describe an analogous operator on the universal enveloping algebra of gl(d), and show why it satisfies a similar property.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
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| 17/02/26 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Rafael Ruggiero | PUC Rio de Janeiro | Seminario di Equazioni Differenziali
Horospherical billiards
We introduce the concept of horospherical billiard in the universal covering of a compact surface without focal points and prove some rigidity results assuming the existence of some geometric first integrals.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027). |
| 17/02/26 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Emmanuel Kowalski | ETH Zürich | Geometry Seminar
Exponential sums, jacobians and graphs
Exponential sums over finite fields are essential ingredients in the solution of many arithmetic problems. Their study often relies on algebraic geometry, and especially on Deligne's Riemann Hypothesis over finite fields, which reveals deep structural features of these sums. In turn, one can exploit these to construct some remarkable combinatorial objects. The talk will provide a survey of these various aspects. (Joint works with A. Forey, J. Fresán and Y. Wigderson)
<em> Note: </em>
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures |