Prossimi Seminari

Martedì 26 Feb ore 11:00
presso Aula Vitali
seminario di algebra e geometria
nel ciclo di seminari
Seminario di Algebra e Geometria
The monodromy group of IHS manifolds of OG10-type
Claudio Onorati
The monodromy group of an IHS manifold is one of the most important tools to investigate their geometry. In the first part of the talk, I will recall the main definitions, giving some motivation. In the second half I will focus on the OG10-type. This is the only type (among the known ones) for which the monodromy group is still a mystery. We explain how to construct new monodromy operators using two families, the O'Grady and the Laza-Saccà-Voisin ones, exhibiting an explicit subgroup of the monodromy group, that we conjecture being all. Time permitting, we will also discuss a geometric constraint to the fact that the monodromy group is smaller than the group of orientation preserving isometries.
Mercoledì 27 Feb ore 14:30
presso Seminario II
nell'ambito della serie
Topics in Mathematics 2018/2019
Introduction to minimax methods
Vittorio Martino
We will introduce the basic tools for the topological methods in critical points theory: the Palais-Smale compactness condition and the deformation lemma. Starting from the finite dimensional case, we will illustrate how the minimax argument works. Eventually, we will show some applications to problems in infinite dimensional setting.
Giovedì 28 Feb ore 16:00
presso Aula Vitali
seminario di analisi matematica
Behaviour of nonlocal sets for small values of the fractional parameter
Claudia Bucur, Università Cattolica del Sacro Cuore
Giovedì 28 Feb ore 16:00
presso Aula seminari - Dipartimento di Scienze Statistiche, I piano
seminario di probabilità
nel ciclo di seminari
Seminari di Probabilità
Density and tube estimates for diffusion processes under Hormander-type conditions
Paolo Pigato (Weierstrass Institute for Applied Analysis and Stochastics, Berlino)
We recall some classic results on the regularity of solutions of stochastic differential equations. Then we consider two specific diffusion processes satisfying hypoellipticity conditions of Hormander type. Using Malliavin Calculus techniques recently developed to deal with degenerate problems, we find estimates for the density of the law of the solution, which we use to prove exponential bounds for the probability that the diffusion remains in a small tube, around a deterministic path, up to a given time. We then present some work in progress on asymptotic sharp estimates for the density and its derivatives for a similar, higher dimensional system.
Lunedì 04 Mar ore 15:00
presso Aula seminari - Dipartimento di Scienze Statistiche, I piano
seminario di probabilità
nel ciclo di seminari
Seminari di Probabilità
Forward or backward simulation? A comparative study
Piergiacomo Sabino (Uniper Global Commodities SE, Dusseldorf)
The aim of this study is to present algorithms for the backward simulation of standard processes that are commonly used in financial applications. We extend the works of Ribeiro and Webber and Avramidis and L’Ecuyer on gamma bridge and obtain the backward construction of a Gamma process. Moreover, we are able to write a novel acceptance-rejection algorithm to simulate Inverse Gaussian (IG) processes backward in time. Therefore, using the time-change approach, we can easily get the backward generation of the Compound Poisson with infinitely divisible jumps, the Variance–Gamma the Normal–Inverse–Gaussian processes and then the time-changed version of the OU process (SubOU) introduced by Li and Linetsky. We then compare the computational costs of the sequential and backward path generation of such processes and show the advantages of adopting the latter one, in particular in the context of pricing American options or energy facilities like gas storages.
Martedì 05 Mar ore 11:00
presso Aula Vitali
seminario di algebra e geometria
Results and problems in Algebraic Combinatorics
Davide Bolognini
In the first part of the seminar, I recall some basic definitions from Commutative Algebra and Combinatorics. In particular, I consider classes of homogeneous ideals arising from discrete structures. The main goal of my research is to describe algebraic properties of these ideals in combinatorial terms. A typical example of this approach is to establish relations between the graded Betti numbers of monomial ideals and the structure of associated simplicial complexes or hypergraphs. In this flavour, I present various results, suggesting also possible future developments. Time permitting, in the last part of the seminar I focus on new directions of research, involving arithmetic matroids and a generalization of flag varieties.
Mercoledì 06 Mar ore 14:30
presso VII piano
nell'ambito della serie
Topics in Mathematics 2018/2019
An introduction to market impact modeling and optimal execution in financial markets
Fabrizio Lillo
Market impact is the response of prices to trades and is a fundamental quantity to understand how supply and demand affect price, but also an important component of transaction costs. In this talk, I introduce the still open problem of mathematical modeling of market impact in a way which is consistent with data but also lacking dynamical arbitrage opportunities. I review some models proposed in the mathematical finance literature and discuss their comparison with data, deriving necessary conditions for the absence of dynamical arbitrage. I then focus on the optimal execution problem in continuous and discrete time, deriving the solution under different specifications of the impact model and of the chosen benchmark.
Mercoledì 06 Mar ore 16:00
presso Aula Seminario VIII piano
seminario di probabilità
McKean-Vlasov stochastic control and Hamilton-Jacobi-Bellman equations on Wasserstein space
Andrea Cosso
Giovedì 07 Mar ore 14:00
presso - Aula Da Stabilire -
seminario di probabilità
Quenched mass transport of particles towards a target
Idris Kharroubi
Giovedì 07 Mar ore 16:00
presso - Aula Da Stabilire -
seminario di probabilità
McKean-Vlasov stochastic optimal control problem
Huyên Pham
Venerdì 08 Mar ore 14:00
presso - Aula Da Stabilire -
seminario di probabilità
Viscosity solutions for PDEs on Wasserstein space
Fausto Gozzi
Martedì 12 Mar ore 11:00
presso - Aula Da Stabilire -
seminario di algebra e geometria
TBA
Roberto Pagaria
TBA
Mercoledì 13 Mar ore 12:00
presso Aula Seminario VIII piano
seminario di probabilità
nel ciclo di seminari
Seminari di Probabilità
Fixed-point theorems and Picard iteration methods for McKean-Vlasov mean-field SDEs with jumps
Stefano Pagliarani - DIES, Università di Udine
We consider a prototype class of Lévy-driven SDEs with McKean-Vlasov (mean-field) interaction in the drift. The coefficient is assumed to be affine in the state-variable and only measurable in the law. We study the equivalent functional fixed-point equation for the unknown time-dependent coefficients of the associated Markovian SDE. By proving a contraction property for the functional map in a suitable normed space, we infer existence and uniqueness results for the MK-V SDE, and derive a discretized Picard iteration method that approximates the law of the solution. Numerical illustrations show the effectiveness of the method, which appears to be appropriate to handle multi-dimensional settings. We finally describe possible extensions and generalizations to more general settings. This talk is based on joint work with Ankush Agarwal.
Mercoledì 13 Mar ore 14:30
presso Seminario II
nell'ambito della serie
Topics in Mathematics 2018/2019
A gentle introduction to matroids
Luca Moci
Matroids axiomatise the notion of linear dependence for a list of vectors. While the applications to computer science and optimization are known since long time, surprising interactions of matroid theory with algebra and algebraic geometry were recently discovered, leading to the proof of important combinatorial conjectures and to the introduction of new matroids invariants. In the first part of the talk I will give an elementary introduction to the topic, focusing on examples arising from graphs and from families of hyperplanes in a vector space.​ In the second part of the talk I will show that the set of (isomorphism classes of) matroids has a natural structure of Hopf algebra. Then I will introduce a class of matroid-like objects, called minor systems, and describe the related bialgebras. This machinery allows to give rise to a wide number of invariants, old and new. (Partially based on joint work with Alex Fink and Clement Dupont)
Giovedì 21 Mar ore 16:00
presso Aula Vitali
seminario di analisi matematica
TBA
Antonio Vitolo
Venerdì 22 Mar ore 14:30
presso Seminario II
seminario di probabilità
On the existence of continuous processes with given one-dimensional distribution
Pietro Rigo
Let $\mathcal{P}$ be the collection of Borel probability measures on $\mathbb{R}$, equipped with the weak* topology, and let $\mu:[0,1]\rightarrow\mathcal{P}$ be a continuous map. Say that $\mu$ is presentable if $X_t\sim\mu_t$, $t\in [0,1]$, for some real process $X$ with continuous paths. It may be that $\mu$ fails to be presentable. Conditions for presentability are given in this note. For instance, $\mu$ is presentable if $\mu_t$ is supported by an interval for all but countably many $t$. In addition, assuming $\mu$ presentable, we investigate whether there is a continuous process $X$ with the same finite dimensional distributions as the quantile process $Q$ induced by $\mu$. The latter is defined, on the probability space $((0,1),\mathcal{B}(0,1),\,$Lebesgue measure$)$, by \begin{gather*} Q_t(\alpha)=\inf\,\bigl\{x\in\mathbb{R}:\mu_t(-\infty,x]\ge\alpha\bigl\}\quad\quad\text{for all }t\in [0,1]\text{ and }\alpha\in (0,1). \end{gather*} Various open problems are stated as well.
Mercoledì 27 Mar ore 14:30
presso - Aula Da Stabilire -
nell'ambito della serie
Topics in Mathematics 2018/2019
TBA
Silvia Benvenuti
TBA
Giovedì 28 Mar ore 16:30
presso Aula Enriques
seminario di analisi matematica
TBA
Stefano Biagi
TBA
Giovedì 02 Mag ore 14:30
presso - Aula Da Stabilire -
nell'ambito della serie
Topics in Mathematics 2018/2019
TBA
Lucia Romani
TBA
Lunedì 13 Mag ore 12:00
presso Seminario I
seminario di probabilità
nel ciclo di seminari
Seminari di Probabilità
Probabilistic results concerning smoothness of the value function and of the free boundary in optimal stopping
Tiziano De Angelis (The University of Leeds)
I will present probabilistic proofs of some regularity properties for the value function of general optimal stopping problems and for the associated optimal boundaries. In particular this talk focusses on C^1 regularity of the value function and Lipschitz continuity of the optimal boundary. Most of our arguments rely on fundamental concepts from the theory of Markov processes and bridge the probabilistic and the analytical strands of the literature on free boundary problems. I will also illustrate situations in which our work improves or complements known facts from PDE theory.
Mercoledì 15 Mag ore 14:30
presso - Aula Da Stabilire -
nell'ambito della serie
Topics in Mathematics 2018/2019
TBA
Andrea Sacchetti
TBA