| 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 |
| 20/03/26 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Victor TURCHIN | Kansas State University |
Joint Topology & Algebra and Representation Theory Seminar (T-ARTS)
"Graph-complexes and rational homotopy theory of embedding spaces"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
The homotopy groups of CW complexes and of the mapping spaces between them are notoriously difficult to compute. However, if one disregards torsion, rational homotopy theory becomes very effective and can easily solve such problems. Moreover, it produces efficient invariants of homotopy classes of maps, called Maurer-Cartan elements, which encode the rational type of path components. I will give a couple of examples and then explain how this extends to embedding spaces.
Based on joint work with Benoit Fresse and Thomas Willwacher.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
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| 20/03/26 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Ben MILLS | York University |
Algebra & Representation Theory Seminar (ARTS)
"Utilising Meta Kazhdan-Lusztig Combinatorics"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Parabolic Kazhdan-Lusztig polynomials are ubiquitous across representation theory, geometry, and Lie theory. This raises two questions: can the (often strictly combinatorial) methods used to compute them be enriched to shed light on algebraic and geometric structures? Furthermore, if two a priori distinct structures are governed by the same polynomials, does this imply a deeper equivalence? <br>
In this talk, we address these questions for parabolic Kazhdan-Lusztig polynomials of type (<em>D<sub>n</sub></em> , <em>A</em><sub><em>n</em>-1</sub>) . By enriching the combinatorial methods to calculate these polynomials, we give a new presentation of the structure for the basic algebra of the anti-spherical Hecke category of isotropic Grassmannians. We then use this enriched structure to prove that it is isomorphic to the type <em>D</em> Khovanov arc algebra.
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<em> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </em>
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| 17/03/26 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Fabrizio Bianchi | Università di Pisa | Seminario di Sistemi Dinamici
Dynamics of Hénon-like maps
Hénon-like maps are invertible holomorphic maps, defined on some convex bounded domain of $mathbb C^k$, that have (non-uniform) expanding behaviour in $p$ directions and contracting behaviour in the remaining $k-p$ directions. They form a large class of dynamical systems in any dimension. In dimension 2, they contain the Hénon maps, which are among the most studied dynamical systems. In this talk, I will give an overview of the main dynamical properties of these maps. In particular, I will focus on how tools from pluripotential theory can allow one to go beyond the algebraic setting of the Hénon maps. The talk is based on joint works with Tien-Cuong Dinh and Karim Rakhimov.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) |
| 17/03/26 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Corentin Fierobe | Università di Roma | Seminario di Sistemi Dinamici
One Can Hear Symmetric Billiard Tables Close to Ellipses
This talk addresses Kac’s famous question, “Can one hear the shape of a drum?”—that is, whether the spectrum of the Laplacian on a domain uniquely determines its shape— in the context of convex planar billiard tables. While non-convex counterexamples are known (Gordon–Webb–Wolpert), the problem remains open for strictly convex domains with smooth boundaries. As shown by Anderson, Melrose, and Guillemin, the spectral question is deeply connected to its dynamical analogue: whether the length spectrum—the set of lengths of all periodic billiard trajectories—determines the domain up to isometry. In joint work with Vadim Kaloshin and Alfonso Sorrentino, we show that this is indeed the case for domains that are sufficiently close to a general ellipse and possess dihedral symmetry.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027). |
| 10/03/26 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Nicola Picenni | Università di Pisa | Seminario di Equazioni Differenziali
A notion of fractional area in codimension 2
We consider a notion of fractional s-area for codimension 2 surfaces in a closed Riemannian manifold or the Euclidean space, which can be seen as an extension of the fractional perimeter to higher codimension. The definition involves a minimum problem over a class of circle-valued maps having prescribed singularities on the given surface.
We discuss various properties of the s-area when s is fixed, and we show that when s tends to 1 it Gamma-converges, with coercivity, to the classical area in the framework of currents.
The talk is based on a joint project with Michele Caselli and Mattia Freguglia.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027). |
| 10/03/26 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Angelica Cueto | Ohio State University | Geometry Seminar
Tritangent planes to space sextic curves: a tropical viewpoint
A classical result due to Clebsch from the mid-nineteenth century confirms that every complex space sextic curve (given as an intersection of a quadric and a cubic surface in projective 3-space) has exactly 120 tritangent planes. In this talk we will show how to use combinatorial methods arising from tropical geometry to revisit this classical problem and perform the analogous count over the reals and extensions thereof. This is joint work with Yoav Len, Hannah Markwig and Yue Ren (arXiv:2512.24277).
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 |
| 09/03/26 | Seminario | 16:00 | 17:00 | 1101 D'Antoni | Bordignon Paolo | Leiden University | DoctorV Seminar
A geometric view on congruences of modular forms
The study of Fourier coefficients of modular forms has a long and rich history, from Ramanujan’s conjectures to the modularity theorem relating modular forms to elliptic curves. In this talk, we first present the arithmetic–geometric viewpoint on modular forms provided by modular curves, and use it to study certain congruences. These may first appear as numerical coincidences, but in fact hide structures arising from the geometry and cohomology of modular curves in p-adic setting. This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) |
| 06/03/26 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Thomas Willwacher | ETH Zürich |
Joint Topology & Algebra and Representation Theory Seminar (T-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.
The talk is based on arXiv:2503.17131 and arXiv:2508.13724.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
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| 06/03/26 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Azzurra CILIBERTI | Ruhr-Universität Bochum |
Algebra and 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.
In the talk, I will present a multiplication formula for cluster characters induced by generating extensions in a gentle algebra A. This formula generalizes a previous result of Cerulli Irelli, Esposito, Franzen, Reineke. Moreover, in the case where A comes from a triangulation T, it provides a representation-theoretic interpretation of the exchange relations in the cluster algebra with principal coefficients in T.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
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