| 18/06/25 | Colloquium | 14:30 | 15:30 | 1201 Dal Passo | Masahiro Yamamoto | the University of Tokyo | COLLOQUIUM DI DIPARTIMENTO
Inverse problems enabling us to detect invisible shapes and properties
NB:This colloquium is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
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| 17/06/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Giulio Galise | La Sapienza Università di Roma | Seminario di Equazioni Differenziali
Liouville theorems for nonlocal operators with conical diffusion
We consider linear stable operators L of order 2s whose spectral measure is positive only in a relative open subset of the unit sphere, the aim being to present Liouville type results, in a half space, for the inequality -Lu ≥ u^p. In particular we will show that u≡0 is the only nonnegative solution for 1 ≤ p ≤ (N+s)/(N-s). The optimality of the exponent (N+s)/(N-s) will also be discussed. Based on a joint work with I. Birindelli and L. Du (Sapienza Università di Roma)
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
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| 12/06/25 | Seminario | 16:00 | 17:00 | 2001 | Amir Vig | University of Michigan, USA | Seminario di Sistemi Dinamici
On the inverse spectral problem for convex planar domains
The inverse spectral problem asks to what extent one can recover the geometry of a manifold from knowledge of either its Laplace spectrum or dynamical counterparts, e.g., the (marked) length spectrum. While counterexamples do exist in general, there are certain symmetry and nondegeneracy conditions under which spectral uniqueness holds. Perhaps the most tantalizing unsolved case is that of strictly convex planar domains, known as Birkhoff billiard tables. It turns out that there is a deep relationship between the Laplace and length spectra, which is encoded in the Poisson relation. In this talk, I will describe my work on both Laplace and length spectral invariants as well as limitations in using the Poisson relation for inverse problems.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027). |
| 12/06/25 | Seminario | 14:30 | 15:30 | 2001 | Stefano Marò | Universidad de Oviedo, Spagna | Seminario di Sistemi Dinamici
Stability of periodic configurations in discrete Lagrangian systems
We consider a class of periodic solutions of second order difference equations with symplectic structure. We obtain an explicit condition for their stability in terms of the 4-jet of the generating function. This result can be seen as a Lagrangian counterpart of the problem of Lyapunov stability of fixed points of area-preserving diffeomorphisms. An application is given to the model of a bouncing ball. Joint work with Rafael Ortega.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027). |
| 11/06/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Andrzej Zuk | Université Paris 7 | Operator Algebras Seminar
From PDEs to groups
Note:
This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
We present a construction which associates to differential equations discrete groups. In order to establish this relation we use automata and random walks on ultra discrete limits. We discuss related results concerning von Neumann dimension and L2 Betti numbers of closed manifolds. |
| 05/06/25 | Seminario | 14:30 | 15:30 | 1200 Biblioteca Storica | Wacław Marzantowicz | U Poznań |
Joint Topology & Algebra and Representation Theory Seminar (T-ARTS)
Reeb graphs and description of homomorphisms onto the free groups
The Reeb graph R(f) of a C^1-function f from M to the real numbers with isolated critical points is a quotient object by the identification of connected components of function levels which has a natural structure of graph. The quotient map p from M to R(f) induces a homomorphism p* from the fundamental group of M to the fundamental group of R(f) which is equal to F_r, the free group of r generators. This leads to the natural question whether every epimorphism from a finitely presented group G to F_r can be represented as the Reeb epimorphism p* for a suitable Reeb (or even Morse) function f. We present a positive answer to this question. This is done by use of a construction of correspondence between epimorphisms from the fundamental group of M to F_r and systems of r framed non-separating hypersurfaces in M, which induces a bijection onto their framed cobordism classes. As applications we provide new purely geometrical-topological proofs of some algebraic facts. |
| 03/06/25 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Navid Nabijou | Queen Mary University of London | Geometry Seminar
Logarithms, orbifolds, negative tangencies
Logarithmic and orbifold structures provide two different paths to the enumeration of algebraic curves with fixed tangencies along a normal crossings divisor. Simple examples demonstrate that the resulting systems of invariants differ, but a more structural explanation of this defect has remained elusive.
I will explain how the two systems of invariants can be identified by passing to an appropriate blowup. This identifies “birational invariance” as the key property distinguishing the two theories. Our proof hinges on a technique – rank reduction – for reducing questions about normal crossings divisors to questions about smooth divisors.
Time permitting, I will discuss extensions of this result to the setting of negative tangencies, where the pathological geometry of the moduli space is controlled using tropical geometry.
This is joint work with Luca Battistella and Dhruv Ranganathan.
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 |
| 27/05/25 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Εfthymios Sofos | Glasgow University | Geometry Seminar
Rational Points on conic bundle surfaces
I will give an introduction to the arithmetic of rational points on surfaces that can be fibred into conics. In the end I will talk about upcoming work with Christopher Frei that uses arguments from analysis to answer some basic questions.
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 |
| 23/05/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Santosha Kumar PATTANAYAK | Indian Institute of Technology - Kanpur |
Algebra & Representation Theory Seminar (ARTS)
"Uniqueness of branching and unique factorization of tensor products of typical representations of Lie superalgebras"
A theorem of Rajan says that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero determines individual constituents uniquely. This is analogous to the uniqueness of prime factorization of natural numbers. We discuss a more general question of determining all the pairs (V1 , V2) consisting of two finite dimensional irreducible representations of a semisimple Lie algebra g such that Res(g0)|V1 ≅ Res(g0)|V2 , where g0 is the fixed point subalgebra of g with respect to a finite order automorphism.
We will also discuss the above tensor product problem in the category of typical representations of basic classical Lie superalgebras.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
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| 22/05/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Tere Seara | UPC Barcelona | Seminario di Sistemi Dinamici
Analytic convex billiards are generically chaotic
In this talk we study chaotic dynamics generated by analytic convex billiards.
We consider the set S of analytic billiards with negative curvature satisfying the following property:
for any rational rotation number, there exists a hyperbolic periodic orbit whose stable and unstable manifolds intersect tansversally along a homolinic orbit.
And we prove that the set S is residual among analytic billiards with negative curvature with the ususal analytic topology.
This result is a consequence of the Baire property and the main result of this work, which reads:
Fixing a rational rotation number p/q, we can prove that the set of analytic billiards with negative curvature having a hyperbolic periodic orbit of rotation umber p/q whose stable and unstable manifolds intersect tansversally along a homolinic orbit, is open and dense.
As a consequence of our results, we have that chaotic billiards are dense among analytic biliards.
Our proof combines Aubry-Mather theory to study periodic orbits of any rotation number as well as their heteroclinic trajectories, with the work by Zehnder on planar twist maps with elliptic points in the 1970's, which provides a methodology for constructing analytic perturbations of maps in order to obtain transversality between the invariant
manifolds of hyperbolic periodic orbits.
This is a joint work with Imma Baldomá, Anna Florio and Martin Leguil.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).
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