Head of Dept: Prof. Giulio Magli
Vice-Head of Dept: Prof. Gabriele Grillo
Department Manager: Dr.ssa Franca Di Censo

### Seminars

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### Upcoming seminars

• Zero-dimensional symmetry, or locally profinite groups
George Willis, University of Newcastle, Australia
giovedì 21 novembre 2019 alle ore 16:00, Aula U5-3014 (Edificio 5, terzo piano) del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca, in Via Cozzi 55
• Un viaggio nel mondo dei poliedri
Giuseppe Conti, Università di Firenze
mercoledì 27 novembre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14
• Propagation of singularities for solutions to Hamilton-Jacobi equations
Piermarco Cannarsa, Università di Roma Tor Vergata
lunedì 2 dicembre 2019 alle ore 15:30, Sala Consiglio del 7 piano, Dipartimento di Matematica, Via Ponzio 31-33, Milano
• Come utilizzare le prove invalsi nella pratica d’aula
Alice Lemmo, Università degli studi dell’Aquila
mercoledì 4 dicembre 2019 alle ore 15:00, Sala Consiglio - piano 7° - edificio 14
• Explainability, intepretability and sensitivity analysis
Emanuele Borgonovo, Department of Decision Sciences, BIDSA, Bocconi University, Milano
venerdì 6 dicembre 2019 alle ore 14:30, Aula Saleri - VI piano
• The mysteries of L-values
Sarah Zerbes, University College London
martedì 10 dicembre 2019 alle ore 14:00, Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50
• Translating cardiac models into the clinic
Steven Niederer, Biomedical Engineering, King’s College London
giovedì 12 dicembre 2019 alle ore 14:00,  Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
• Long-time asymptotics for evolutionary crystal dislocations models
Matteo Cozzi, University of Bath
martedì 17 dicembre 2019 alle ore 15:30, Aula seminari 3° piano
• Nonlinear Peridynamic Models
Giuseppe Maria Coclite, Politecnico di Bari
mercoledì 22 gennaio 2020 alle ore 15:15, Aula seminari 3° piano

### Past Seminars

• ON A MATHEMATICAL THEORY OF REPEATED QUANTUM MEASUREMENTS
Vojkan Jaksic, McGill University
giovedì 13 giugno 2019 alle ore 14:30 precise, Aula Seminari III piano
ABSTRACT
The statistics of the (finite alphabet) outcomes of repeated quantum measurements is studied by methods of thermodynamic formalism. Viewed as one-dimensional spin systems with long range interactions, repeated quantum measurements exhibit very rich (and sometimes very singular) thermodynamic behaviour. We will describe general thermodynamical formalism of these systems and illustrate its unexpected features on a number of examples.
• Multiphase flow in heterogeneous geologic media
Stephan K. Matthai, Chair of Reservoir Engineering, Department of Infrastructure Engineering, The University of Melbourn
giovedì 13 giugno 2019 alle ore 14:00, Aula consiglio VII piano, Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
Heterogeneous permeability, porosity, capillary pressure and mechanical properties are key characteristics of sedimentary and volcanic rocks with sufficient interconnected pores to permit fluid flow. In many cases, heterogeneities are nested, for instance, where mm-scale laminations define the internal structure of bed-forms that combine into facies associations and facies distributions on the km scale. Where such rocks have experienced an overprint by deformation or reactive fluid flow, initial heterogeneities might have been amplified even further. Thus, fracturing can impart long-range spatial correlations on the permeability structure, strongly amplifying permeability anisotropy, even without a noticeable increase in the porosity.
This presentation examines the impact of such nested heterogeneities on flow, (reactive) transport, and multiphase fluid displacement in natural heterogeneous porous media. The emphasis will be on intermediate scale features (~0.1 - 500-m in size) that are difficult to investigate in the laboratory or in the subsurface because flow patterns cannot be resolved by geophysical imaging techniques. The investigative method used here are field-data based hybrid FEM-FVM numeric simulations where an operator splitting technique is employed, solving elliptic-parabolic equations (fluid pressure, temperature, chemical diffusion) with the FEM and the hyperbolic ones (multiphase flow and tracer transport) with the FVM.
The presentation will illustrate the behaviour of the heterogeneous systems and the numeric methods used to model them, proceeding from tracer transport, to gas injection and water flooding of naturally fractured reservoirs to maximise hydrocarbon recovery. The presentation will conclude with a general discussion of the impact of heterogeneity, addressing questions such as: given the nested nature of geologic heterogeneity, is the spreading of gas plumes ergodic? – or – in view of the impact of heterogeneity on sweep, how can gas storage or hydrocarbon recovery be maximised?

Contatto: paolo.zunino@polimi.it
• 'Strange' rational maps and spectra of graphs and groups
Rostislav Grigorchuk, Texas A&M University
giovedì 13 giugno 2019 alle ore 16:30 precise, 'Aula U5-3014 (Edificio 5, terzo piano) del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca, Via Cozzi 55
ABSTRACT
I will present a few results concerning spectral theory of
graphs and groups that are based on the use of multidimentional rational
maps and self-similar groups. It will be explained how these maps
appear, how they help to compute the spectrum, and why they are
strange'' (or better to say, non typical). As part of the story there
will be a short survey on spectra of infinite graphs and groups with
some old and new results belonging to the speaker and his collaborators
(L.Bartholdi, A.Dudko, D.Lenz, T.Nagnibeda, B.Simanek, A.Zuk). The
relation to the random Schrodinger operator will be mentioned at the end
of the talk if time permits.
• Symmetry preservation for fourth order eigenvalue optimization problems
Francesca Colasuonno, Università degli Studi di Torino
mercoledì 12 giugno 2019 alle ore 15:15, Aula seminari 3° piano
ABSTRACT
In this talk, we will discuss some recent results on two eigenvalue optimization problems governed by the biharmonic operator, under Dirichlet or Navier boundary conditions. From a physical point of view, in two dimensions our problem corresponds to building a plate, of prescribed shape and mass, out of materials with different densities --varying in a certain range of values-- in such a way to minimize the lowest frequency of the body. This problem is also referred to as composite plate problem. Both for the clamped plate (i.e., Dirichlet b.c.) and for the hinged plate (i.e., Navier b.c.), we will prove the existence of an optimal configuration and give an explicit representation of the minimizing densities in terms of sublevel sets of their corresponding first eigenfunctions. Finally, we will discuss symmetry preservation properties of the optimal configurations, in the presence of some symmetry and convexity of the domain. The tools used differ depending on the boundary conditions: while the hinged plate problem inherits the maximum principles for second order elliptic systems, allowing us to exploit the moving plane method to get symmetry preservation in more general domains, the situation is more complicated for the clamped plate problem, where we will use the polarization technique and the properties of the Green's function to deal with radial symmetry preservation in a ball.
This talk is based on two joint papers with Eugenio Vecchi (Trento).
• Nonparametric methods for complex spatial domains: density estimation and hypothesis testing
Federico Ferraccioli, Università degli Studi di Padova
martedì 11 giugno 2019 alle ore 14:15, Aula consiglio VII piano, Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
ABSTRACT
I will present different nonparametric methods for data distributed over complex spatial domains. First I will consider the problem of density estimation. Specifically I will propose a nonparametric penalized likelihood approach for data distributed over planar domains with complex geometries. The model formulation is based on a regularization with differential operators, and it is made computationally tractable by means of finite elements. In this setting, I will describe a permutation procedure for one and two samples hypothesis testing. Then I will consider hypothesis testing procedures in the case of spatial regression models with differential regularization. In particular, I will propose a test based on sign-flipping. I will present the performances of the proposed methods via simulation studies and application to real data.

Contatto: laura.sangalli@polimi.it

• Superoscillations and approximation of generalized functions
Daniele Struppa, Chapman University
lunedì 10 giugno 2019 alle ore 15:15 precise, Sala Consiglio, 7 piano, Edificio La Nave, Via Ponzio 31-33
ABSTRACT
This talk offers an introductory look at how superoscillatory sequences can be utilized to approximate generalized functions. After an introduction to superoscillations, I will briefly discuss how such sequences can be used to approximate tempered distributions, and will then focus on their role in the context of the theory of hyperfunctions. The talk will be based on a series of papers jointly coauthored with F.Colombo, I.Sabadini, and A.Yger.
• On the quasistatic limit for a debonding model in dimension one; a vanishing inertia and viscosity approach
Filippo Riva, SISSA
giovedì 6 giugno 2019 alle ore 15:15, Aula seminari 3° piano
ABSTRACT
In the theory of linearly elastic fracture mechanics one-dimensional debonding models, or peeling tests, provide a simplified but still meaningful version of crack growth models based on Griffith's
criterion. They are both described by the wave equation in a time-dependent domain coupled with suitable energy balances and irreversibility conditions.Unlike the general framework, peeling tests allow to deal with a
natural issue of great interest arising in fracture mechanics. It can be stated as follows: although all these models are dynamic by nature, the evolution process is often assumed to be quasistatic (namely the
body is at equilibrium at every time) since inertial effects can be neglected if the speed of external loading is very slow with respect to the one of internal oscillations. Despite this assumption seems to
be reasonable, its mathematical proof is really far from being achieved.In this talk we validate the quasistatic assumption in a particular damped debonding model, showing that dynamic evolutions converge to the quasistatic one as inertia and viscosity go to zero. We also highlight how the presence of viscosity is crucial to get this kind of convergence.
• Robin eigenvalues on domains with cusps
Hynek Kovarik, Università degli studi di Brescia
giovedì 6 giugno 2019 alle ore 14:00, Aula seminari 3° piano
ABSTRACT
We consider the Laplace operator with the Robin boundary condition with negative coefficient
on bounded domains with cusps. We show that if the cusps is not too strong, then the operator is bounded from below and calculate the leading term in the asymptotic expansion of its negative eigenvalues as the coefficient of the boundary condition tends to infinity. This is a joint work with Konstantin Pankrashkin.