Seminari/Colloquia
Pagina 1
Date  Type  Start  End  Room  Speaker  From  Title 

13/09/24  Seminario  16:00  17:00  1201 Dal Passo  "Graph Cohomologies, Matroids and Coloring" N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
A celebrated result in graph theory links the chromatic polynomial of a graph to the Tutte polynomial of the associated graphic matroid. In 2005, HelmeGuizon and Rong proved that the chromatic polynomial is categorified by a cohomological theory called chromatic cohomology.
In this talk, I will describe how to associate a matroid to a directed graph G, called the multipath matroid of G, which encodes relevant combinatorial information about edge orientation. We also show that a specialization of the Tutte polynomial of the multipath matroid of G provides the number of certain "good" digraph colorings. Finally, analogously to the relationship between the chromatic polynomial and chromatic cohomology, I will show how the polynomial expressing the number of "good" digraph colorings is linked to multipath cohomology, introduced in a work with Caputi and Collari in 2021.  
13/09/24  Seminario  14:30  15:30  1201 Dal Passo  "On the representation theory of generalized small quantum group" N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
The small quantum groups u_{q}(g) are finitedimensional quotients of quantum universal enveloping algebras U_{q}(g) at a root of unity q for g a semisimple complex Lie algebra. After the work of Lusztig, the representation theory of these quantum objects was intensively studied because of its relation with the representation theory of semisimple algebraic groups in positive characteristic. In this talk, I will present some results on the representation theory of what we call "generalized" small quantum groups. A particular feature of these objects is that the role of the corresponding Cartan subalgebra is played by a finite nonabelian group. Nevertheless, they still admit a triangular decomposition and share similar properties with the standard quantum groups, like the existence of weights (that are no longer onedimensional) and Verma modules.
This talk is based on a joint work with Cristian Vay [Simple modules of small quantum groups at dihedral groups, Doc. Math. 29 (2024), 138].  
04/09/24  Seminario  14:30  15:30  1201 Dal Passo  Deepesh Toshniwal  Delft University of Technology  A local L^{2}stable projector for Truncated Hierarchical Bsplines
Isogeometric Analysis (IGA) advocates for the direct utilization of splinebased geometric representations for performing splinebased numerical simulations. Over the last decade and a half, this philosophy has been applied to diverse applications with great success and has yielded theoretical developments that cement the status of smooth splines as excellent tools for approximation. In this talk I will focus on the use of Truncated Hierarchical Bspline (THBspline) spaces and discuss the formulation of a local, L^{2}stable projector for them. The projector is an extension of the Bézier projection proposed by Thomas et al. (2015) and relies on a characterization of linear independence of THBsplines over certain macroelements.
This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).

29/07/24  Seminario  14:30  15:30  1201 Dal Passo  Marianne Déglise  ENS Paris Saclay  Combinatorial study of coefficients of the decomposition theorem for universal linear degenerations
We study a geometric/combinatorial characterisation of supports for linear degenerations of flag varieties in an attempt to determine the coefficients of the decomposition theorem. We show that it behaves correctly when applying the operation suspension, and obtain positive results in the PBWlocus.

10/07/24  Seminario  16:00  17:00  1201 Dal Passo  Leonardo Sangaletti  University of Leipzig  An L4 quantum energy inequality for the thermal sector
Energy density and its positivity properties represent a fundamental subject in classical and quantum physics. In this talk, we will investigate this topic in the thermal representation of a free massive quantum scalar field. After a brief review of the fundamental mathematical tools at the base of this work, we will construct the GNS representation of our QFT induced by a state at thermal equilibrium (KMS). Therein, we will identify the generator of the time evolution and its spatial density. The symmetry between the "particles" and "holes" makes evident the impossibility for a lower bound for the expectation value of the energy density in this representation. In order to tackle this problem, we will investigate and extend some results of modular theory and noncommutative Lp spaces. In this way, we will obtain a general result concerning the expectation value of operators affiliated to a von Neumann algebra. Finally, the proven results will be applied to our setting to derive an L4 state dependent nontrivial QEI.
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0 
09/07/24  Seminario  14:30  15:30  1201 Dal Passo  Maria Michaela Porzio  Sapienza Università di Roma  The role of the data on the regularity of the solutions to some non singular parabolic equations
In this talk we describe the influence of the initial data and the forcing terms on the regularity of the solutions to a class of evolution equations including the heat equation, linear and semilinear parabolic equations, together with the nonlinear pLaplacian equation. We focus our study mainly on the regularity (in terms of belonging to appropriate Lebesgue spaces) of the gradient of the solutions.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006 
05/07/24  Seminario  16:00  17:00  1201 Dal Passo  Ping Xu  U Penn State  Derived differentiable manifolds
One of the main motivations behind derived differential geometry is to deal with singularities arising from zero loci or intersections of submanifolds. Both cases can be considered as fiber products of manifolds which may not be smooth in classical differential geometry. Thus, we need to extend the category of differentiable manifolds to a larger category in which one can talk about "homotopy fiber products". In this talk, we will discuss a solution to this problem in terms of dg manifolds. The talk is mainly based on a joint work with Kai Behrend and HsuanYi Liao.

05/07/24  Seminario  14:30  15:30  1201 Dal Passo  Mathieu Stiénon  U Penn State  Formal geometry of groupoids
I will give a brief survey of the formal geometry of groupoids.

03/07/24  Seminario  16:00  17:00  1201 Dal Passo  Vedran Sohinger  University of Warwick  Invariant measures as probabilistic tools in the analysis of nonlinear ODEs and PDEs
Gibbs measures for nonlinear dispersive PDEs have been used as
a fundamental tool in the study of lowregularity almost sure
wellposedness of the associated Cauchy problem following the pioneering
work of Bourgain in the 1990s. In the first part of the talk, we will
discuss the connection of Gibbs measures with the KuboMartinSchwinger
(KMS) condition. The latter is a property characterizing equilibrium
measures of the Liouville equation. In particular, we show that Gibbs
measures are the unique KMS equilibrium states for a wide class of
nonlinear Hamiltonian PDEs. Our proof is based on Malliavin calculus and
GrossSobolev spaces. This is joint work with Zied Ammari.
In the second part of the talk, we will explain a general principle that allows us to obtain almost sure global solutions for Hamiltonian PDEs provided that one has a stationary probability measure. In this context, stationarity refers to a solution of the associated Liouville equation. This more general notion replaces the invariance from before. The second part of the talk is joint work with Zied Ammari and Shahnaz Farhat. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0 
21/06/24  Seminario  14:30  15:30  1101 D'Antoni  Adam Doron  Haifa University  Arveson's hyperrigidity conjecture is false
A classical result in approximation theory due to Korovkin asserts that a sequence of positive unital maps on C([0,1]) converges pointwise to the identity if they merely converge to the identity on the functions 1,x,x^2. This result was later generalized by Saskin, who showed that convergence to the identity on a generating function system implies convergence to the identity everywhere if and only if the system has full Choquet boundary.
Arveson's last open conjecture in his seminal work on noncommutative boundary theory predicts that a noncommutative analogue of Saskin's result holds. We refute Arveson's conjecture with an elementary counterexample. All notions will be explained during the talk.
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0 
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