| 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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| 18/03/26 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Robert Simon | London School of Economics and Political Science |
Operator Algebras Seminar
Paradoxical decompositions as the only solutions to locally finite conditions
Note:This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Assuming g_1, g_2, ..., g_k are measure preserving transformations on a probability space X, we require that a function f from X to a measurable space Y satisfies that f(x) is in F(x, f(g_1 x), .... f(g_k x) ) almost everywhere for an upper semi continuous correspondence F defined on X x Y^k. If there exists such functions however NONE of them are measurable with respect to any finitely additive extension of the probability measure for which the g_i are still measure preserving, we say that the correspondence F is paradoxical. We demonstrate some paradoxical correspondences that are also convex valued and nowhere empty. We are curious if there are applications beyond optimization and economics. |
| 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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| 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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