### Seminari

### Prossimi Seminari

**Dealing with unreliable computing platforms at extreme scale**

Luc Giraud, INRIA (Inria Bordeaux – Sud-Ouest)

mercoledì 23 gennaio 2019 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Poroelasticity: Discretizations and fast solvers based on geometric multigrid methods**

Francisco José Gaspar Lorenz, Department of Applied Mathematics -Zaragoza University – Spain

giovedì 31 gennaio 2019 alle ore 14:00, Sala Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Application of Polyconvexity and multivariable convexity of energy potentials in nonlinear solid mechanics**

Javier Bonet, University of Greenwich

giovedì 14 febbraio 2019 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

### Seminari Passati

**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.

**Approximating the true time weighted return**

Marco Guzzetti, Politecnico di Milano

mercoledì 20 giugno 2018 alle ore 12:15 precise, Aula seminari del Terzo piano**Bridgeland stability and the genus of space curves**

Emanuele Macrì, Northeastern University, Department of Mathematics

martedì 19 giugno 2018 alle ore 14:30 precise, Aula seminari del terzo pianoABSTRACTI will give an introduction to various notions of stability in the bounded derived category of coherent sheaves on the three-dimensional projective space. As application I will show how to possibly use these techniques towards the study of space curves. This is joint work with Benjamin Schmidt.