### Seminari

### Prossimi Seminari

**Laser "su misura" per il trattamento di tumori**

Paola Saccomandi, Politecnico di Milano

mercoledì 27 marzo 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Some remarks on the forces exerted by a viscous fluid on a bluff body**

Gianmarco Sperone, Politecnico di Milano

giovedì 28 marzo 2019 alle ore 15:15, Aula seminari 3° piano**Simplicial splines for representation of density functions**

Karel Hron e Jitka Machalova, Palacky University di Olomouc

martedì 2 aprile 2019 alle ore 15:00 precise, Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14**Stima del valore aggiunto di scuola: stato dell'arte del modello INVALSI e prospettive. Quali implicazioni di policy?**

Tommaso Agasisti, Politecnico di Milano

mercoledì 3 aprile 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**On the modelling of particle and pedestrian motion with Fokker-Planck equations**

Alfio Borzì, University of Wuerzburg -Germania-

giovedì 4 aprile 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Problemi di frontiera libera nelle scienze applicate**

Sandro Salsa, Politecnico di Milano

mercoledì 10 aprile 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Errori sistematici e confondimento degli studi osservazionali basati sui dati dal mondo reale**

Giovanni Corrao, Università degli Studi di Milano-Bicocca

mercoledì 8 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Inverse Problems in Adaptive Optics**

Ronny Ramlau, RICAM, Austrian Academy of Sciences, Linz, Austria

mercoledì 8 maggio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Forma e complessità in Natura: perché il mondo è matematico?**

Pasquale Ciarletta, Politecnico di Milano

mercoledì 15 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Matematica, società, economia e sviluppo**

Giulia di Nunno, University di Oslo

mercoledì 22 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Comunicare il progetto. Storytelling e tecniche di rappresentazione**

Francesca Piredda, Politecnico di Milano

mercoledì 29 maggio 2019 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Semi-implicit finite-volume integrators for all-scale atmospheric dynamics**

Piotr Smolarkiewicz, European Centre for Medium-Range Weather Forecasts, Reading, Berkshire, United Kingdom

giovedì 30 maggio 2019 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

### Seminari Passati

**Space-Time Adaptive THMC Simulation with Hybrid FEM-FVM Methods Applied to CO2 Geo-Sequestration**

Stephan Matthai, Peter Cook Centre for CCS, The University of Melbourne at Parkville, VIC 3010, Australia

giovedì 27 settembre 2018 alle ore 14:00, Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14ABSTRACTModelling the highly localised plume spreading during CO2 geo-sequestration using conventional synchronous time-driven simulation (TDS) has been impeded by the stringent Courant-Fredrich-Levy (CFL) condition, which leads to an excessive number of time steps and consequently long computing times. To overcome this problem, we present an asynchronous discrete event simulation (DES) scheme based on local time stepping criteria, specifically developed for the CSMP++ CO2 geo-sequestration simulator. The proposed DES method is applied to a complex and heterogeneous heuristic CO2 storage model, where it proves that DES is able to concentrate the computational effort on the active regions where fast CO2 flow occurs. As a result, the execution time for the modelling of a 5-year injection is significantly reduced from over 91 days (estimated for TDS) to only 0.5 days. This dramatic speedup facilitates the modelling of CO2 injection and long-term plume spreading behaviours at the scales of field storage sites. The benefits of the new method scale with the level of refinement of geologic detail and include a distinct increase in the level of physical realism of the simulations because fast and slow events are equally well resolved in contrast with TDS implicit schemes which are robust, but fail to resolve the events captured by the new asynchronous scheme.

Contact: paolo.zunino@polimi.it

**Coupled problems in Environmental and medical applications**

Hiroshi Suito, Mathematical Science Group, Advanced Institute for Materials Research, Tohoku University, Japan

martedì 18 settembre 2018 alle ore 14:00, Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTFluid–structure interaction (FSI) problems arise under various circumstances including environmental and medical applications. This talk firstly presents numerical simulations for motions of aquatic plants interacting with surrounding fluids using immersed boundary method (IBM) with finite-difference approximation on fixed meshes. We also present simulations for blood flows in aorta solved on finite-element meshes moving with the vessel wall. Aortic aneurysms and aortic coarctations are considered here. Geometrical characteristics such as curvature and torsion help us to understand the essential difference for morphologies among patients. The latter problem is followed by a machine learning approach by which wall shear stress and oscillatory shear index distributions are estimated using geometrical characteristics of the vessels.

Contact: alfio.quarteroni@polimi.it

**An inverse boundary value problem arising from cardiac electrophisiology**

Luca Ratti, Politecnico di Milano

martedì 18 settembre 2018 alle ore 15:15, Politecnico di Milano, Dipartimento di Matematica, Aula Seminari 3° PianoABSTRACTThe cardiac electrical activity can be comprehensively described throughout the monodomain model, consisting of a semilinear parabolic equation coupled with a nonlinear ordinary differential equation.

In my talk, I will introduce the inverse problem of identifying conductivity inhomogeneities in the monodomain system, taking advantage of data acquired on the boundary of the domain. Due to the complexity of the task, I will first tackle the stationary counterpart of the problem, regarding which it is possible to formulate well-posedness results both for the forward and for the inverse problem, and to rigorously introduce reconstruction procedures. Similar results are then generalized to the full complexity of the original model.

Throughout the presentation, I will focus on the problem of localizing small size inhomogeneities, as well as arbitrarily large ones, by means of the constraint optimization of a suitable misfit functional. The first task is achieved by relying on an asymptotic expansion of the boundary voltage with respect to the size of the inclusion, and employing tools from the topological optimization theory. The second issue is analyzed by means of the regularization theory of inverse problems and introducing a convenient relaxation of the optimization problem. The theoretical results are supported by numerical experiments, which are exhaustively reported.

This is a joint work with Elena Beretta, Cristina Cerutti, Cecilia Cavaterra, Andrea Manzoni and Marco Verani.**Rotation number of the linear Schrödinger equation with discontinuous almost periodic potentials**

Zhe Zhou, Chinese Academy of Sciences, Beijing

giovedì 13 settembre 2018 alle ore 15:00, Aula Seminari 3° pianoABSTRACTIn this talk, based on the celebrated paper [R. Johnson and J. Moser, Comm. Math. Phys., 1982], we will recover the rotation numbers of the Schrödinger equation. The essential elements in the proof are positive homogeneity and almost periodicity. From this point of view, the concept of rotation numbers may be introduced in the case of discontinuous potentials. Moreover, we will show the optimal estimate of rotation numbers in such case.**KöNIG'S PROBLEM FOR ABELIAN PERMUTATION GROUPS**

Andrzej Kisielewicz, Uniwersytet Wroc?awski, Wydzia? Matematyki i Informatyki

martedì 11 settembre 2018 alle ore 14:15, Aula seminari III pianoABSTRACTKönig's problem for permutation groups concerns the following question: Given a permutation group P = (P, X) acting on a finite set X, is there a graph G=(G, X) with the set of vertices X, such its automorphisms are precisely permutations in P? König's problem is to find a necessary and sufficient conditions for a permutation group P to be the automorphism groups of some graph.

There exist permutation groups that are not the automorphism groups of any graph (for example, alternating groups or groups generated by a single cyclic permutation). So far, this version of König’s problem (known also as the concrete version) has been solved only for regular permutation groups, cyclic permutation groups (generated by a single permutation), and partially, for abelian permutation groups.

In this talk we demonstrate however that the result by Zelikovskij [3] concerning König's problem for abelian permutation groups, reported in a recent survey [2], is false. We argue that a more natural setting for this problem is that concerning the automorphism groups of edge-colored graphs. Our main result, based on techniques applied in [1], provides a characterization of those abelian permutation groups that are the automorphism groups of edge-colored graphs and shows, in addition, that each such group can be represented by an edge-colored graph using no more than 4 colors.

References

[1] M. Grech, A. Kisielewicz, Symmetry groups of boolean functions, European J. Combin. 40 (2014) 1-10.

[2] J. Morris, Automorphism Groups of Circulant Graphs - a Survey, in: Bondy A., Fonlupt J., Fouquet JL., Fournier JC., Ramrez Alfonsn J.L. (eds) Graph Theory in Paris. Trends in Mathematics. Birkhuser Basel 2006, pp. 311-325.

[3] A. Z. Zelikovskij, Konigs problem for Abelian permutation groups, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk 5 (1989), 34-39.**A new paradigm for geometric modeling: Pythagorean Hodograph (PH) B-Spline curves**

Gudrun Albrecht, National University of Colombia

martedì 31 luglio 2018 alle ore 14:00, Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14ABSTRACTWe introduce the new class of planar Pythagorean-Hodograph (PH) B–Spline curves. They can be seen as a generalization of the well-known class of planar Pythagorean-Hodograph (PH) Bézier curves, presented by R. Farouki and T. Sakkalis in 1990, including the latter ones as special cases. Pythagorean-Hodograph B–Spline curves are nonuniform parametric B–Spline curves whose arc-length is a B–Spline function as well. An important consequence of this special property is that the offsets of Pythagorean-Hodograph B–Spline curves are non-uniform rational B–Spline (NURBS) curves. Thus, although Pythagorean-Hodograph B–Spline curves have fewer degrees of freedom than general B–Spline curves of the same degree, they offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. After providing a general definition for this new class of planar parametric curves, we !

present useful formulae for their construction and discuss their remarkable attractive properties. Then we provide a method to determine within the set of all PH B–Splines the one that is closest to a given reference spline having the same degree and knot partition.

Contact franca.calio@polimi.it

**Optimal control of treatment time in a diffuse interface model of tumor growth and related issues**

Elisabetta Rocca, Università di Pavia

giovedì 28 giugno 2018 alle ore 11:15, Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14ABSTRACTWe consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient and surrounded by host tissue. The introduction of cytotoxic drugs into the system serves to eliminate the tumor cells and in this setting the concentration of the cytotoxic drugs will act as the control variable. Furthermore, we allow the objective functional to depend on a free time variable, which represents the unknown treatment time to be optimized. As a result, we obtain first order necessary optimality conditions for both the cytotoxic concentration and the treatment time

Contact: pasquale.ciarletta@polimi.it

**VAPORIZING AND FREEZING THE RIEMANN ZETA FUNCTION**

Terence Tao, University of California, Los Angeles

venerdì 22 giugno 2018 alle ore 14:30, Edificio U4, P.zza della Scienza, 4, Aula Luisella SironiABSTRACTIn 1950, de Bruijn studied the effect of evolving the Riemann zeta function (or more precisely, a closely related function known as the Riemann xi function) by the (backwards) heat equation. His analysis, together with later work by Newman, showed that there existed a finite constant Lambda, at most 1/2 in value, such that the Riemann hypothesis for this evolved function was true at times greater than or equal to Lambda, and false below that threshold. Thus the Riemann hypothesis for the zeta function is equivalent to Lambda being non-positive. Recently, in joint work with Brad Rodgers, I was able to establish the complementary estimate that Lambda is non-negative, confirming a conjecture of Newman; thus, the Riemann hypothesis for zeta, if true, is only "barely so". The proof relies on an analysis of the dynamics of zeroes of entire functions under heat flow; it turns out that as one evolves forward in time, the zeroes "freeze" into approximate arithmetic progressions, while if one evolves backwards, the zeroes "vaporize" to leave the critical line. In followup work in an online collaborative "Polymath" project, the upper bound on Lambda has also been improved. We describe these results and their proofs in this talk.