Seminari/Colloquia

Pagina 15


DateTypeStartEndRoomSpeakerFromTitle
06/02/24Seminario14:3016:001101 D'AntoniRoberto VaccaUniversità di Roma Tor VergataSome examples of Ulrich sheaves

In this talk we will introduce Ulrich sheaves on projective algebraic varieties. The corresponding notion for modules over rings originated from the work of Ulrich, but only after a paper by Eisenbud and Schreyer its geometric side received many attention due to the connection with determinantal and Pfaffian representations of (Chow forms of) varieties. The main questions are existence of such sheaves and, if so, their minimal rank. Positive answer to the first question is known for curves, surfaces (up to change of polarization), Veronese varieties, Segre varieties and complete intersections. Outside those examples, very few is known in dimension at least 3; therefore we will focus on Fano 3-folds.
02/02/24Seminario16:0017:001201 Dal Passo
Giovanni CERULLI IRELLI
"Sapienza" Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Specialization map for quiver Grassmannians"

  We define a specialization map for quiver Grassmannians of Dynkin type and prove that it is surjective in type A. This generalizes a beautiful theorem of Lanini and Strickland concerning the cohomology of degenerate flag varieties.
  This is a joint ongoing work with Francesco Esposito, Ghislain Fourier and Fang Xin.
02/02/24Seminario14:3015:301201 Dal Passo
Roberto FRINGUELLI
"Sapienza" Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Zastava Spaces via non-degenerate maps"

  Let k be a field, G be a reductive group over k, B be a Borel subgroup of G and C be a smooth curve over k. The B-orbit stratification of the flag variety G/B induces a natural stratify-cation on the moduli space of maps from C to G/B . The open stratum is strictly related to the so-called Zastava spaces.
  In this talk, we give an overview of the main properties of these spaces. If time permits, we also present some consequences on the moduli space of G-bundles.
30/01/24Seminario16:0017:001201 Dal PassoDaniele CastorinaUniversità di Napoli Federico II
Seminario di Equazioni Differenziali
Mean field sparse optimal control of systems with additive white noise

We analyze the problem of controlling a multi-agent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with a SDE constraint, we introduce a rigorous limit process towards an infinite dimensional optimal control problem constrained by the coupling of a system of ODE for the leaders with a McKean-Vlasov-type SDE, governing the dynamics of the prototypical follower. The latter is, under some assumptions on the distribution of the initial data, equivalent with a (nonlinear parabolic) PDE-ODE system. The derivation of the limit mean-field optimal control problem is achieved by linking the mean-field limit of the governing equations together with the Gamma-limit of the cost functionals for the finite dimensional problems. Joint work with Giacomo Ascione (SSM Napoli) and Francesco Solombrino (Napoli Federico II).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006
30/01/24Seminario14:3016:001101 D'AntoniLuca BattistellaUniversità di BolognaHyperelliptic curves and differentials

Strata of differentials have been studied from several perspectives, from dynamics to geometry and topology. Algebraic geometers need compactifications. One, which is a posteriori logarithmic, was introduced by Bainbridge--Chen--Gendron--Grushevsky--Möller in terms of multiscale (collections of) differentials (on reducible nodal curves). This natural compactification is unfortunately not irreducible, but they were able to single out the main component in terms of a condition on global residues; their proof rests on transcendental methods. I will mention a conjecturally equivalent condition which is purely algebraic. In joint work with Sebastian Bozlee, we give a proof of concept of this conjecture in the case of hyperelliptic differentials. The technical core of our work is a flexible tool for constructing hyperelliptic Gorenstein contractions of reducible nodal curves, given a hyperelliptic tropical differential, i.e. a suitable piecewise-linear function, on the dual graph.
26/01/24Colloquium14:3015:301201 Dal PassoKevin BuzzardImperial College LondonFormalising modern research mathematics

A few years ago, the idea of formalising modern research level mathematics seemed completely out of reach. Since then, more and more examples have appeared. I'll go through several examples (some related to the mathematics of Scholze, Tao and Gowers), and talk about how the process is evolving, enabling multiple people to collaborate in the formalisation of modern research in real time. Computer-verified proofs: 48 hours in Rome
25/01/24Seminario14:3015:301201 Dal PassoGihan MarasinghaUniversity of ExeterThe benefits and challenges of teaching proof with Lean

This presentation will explore the pivotal role of the Lean in enhancing first-year undergraduates' understanding of mathematical proofs. I will share insights from my experiences and initial educational research on teaching a large first-year undergraduate cohort with Lean, focusing on how this tool can significantly impact student perception of proofs. Additionally, I will address the challenges encountered in teaching with Lean and the implications for learning and comprehension. Computer-verified proofs: 48 hours in Rome
25/01/24Seminario12:0013:001201 Dal PassoFloris van DoornUniversity of BonnThe internals of Lean

In this talk I will describe what goes on behind the scenes of Lean. I will explain the logic of Lean, called dependent type theory, what Lean tactics are and explain why we can trust proofs that are checked by Lean. Computer-verified proofs: 48 hours in Rome
24/01/24Seminario15:3016:301201 Dal PassoFilippo A. E. Nuccio Mortarino Majno di CapriglioUniversité Jean Monnet Saint-ÉtienneHow to enjoy a mathematical discussion with your laptop

In this talk I will illustrate how certain programs, of which Lean is an example, permit to interact with a computer about the logical soundness of mathematical arguments. I will go through the details of well-known proofs trying to understand the feedback provided by the computer and will try to share the fun involved in the process. Computer-verified proofs: 48 hours in Rome
23/01/24Seminario14:3016:001101 D'AntoniMichele PerniceKTH (Stockholm)A stacky Castelnuovo's contraction theorem

In this talk, we are going to discuss a generalization to weighted blowups of the classical Castelnuovo' contraction theorem. Moreover, we will show as a corollary that the moduli stack of n-pointed stable curves of genus 1 is a weighted blowup. This is a joint work with Arena, Di Lorenzo, Inchiostro, Mathur, Obinna.

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