Seminars in Mathematical Sciences

No upcoming seminars have been scheduled (not unusual outside term time).

Usual Venue: MCS2068

Apr 28 13:00 Alexandre Girouard (Université Laval): Isoperimetric-type upper bounds for Steklov eigenvalues of warped products

We obtain isoperimetric-type upper bounds for the Steklov eigenvalues of Riemannian warped products \(D\times_h\Sigma\), where \(D\) is compact with boundary and \(\Sigma\) is closed. The bounds depend on volume, dimension and \(L^p\) norms of the warping function \(h\). The bounds are sharp and in some cases we obtain quantitative stability improvement. Homogenization theory will play a role in saturating some bounds. I will compare this use of homogenization theory to some of its other uses in spectral geometry. This is based on joint work with Jade Brisson, Bruno Colbois, Katie Gittins and Jean Lagacé.

Venue: MCS2068

May 05 13:00 Yufei Zhang (Imperial College London): Continuous-time mean field games: a primal-dual characterization

This paper establishes a primal-dual formulation for continuous-time mean field games (MFGs) and provides a complete analytical characterization for the set of all Nash equilibria (NEs). We first show that for any given mean field flow, the representative player’s control problem with measurable coefficients is equivalent to a linear program over the space of occupation measures. We then establish the dual formulation of this linear program as a maximization problem over smooth subsolutions of the associated Hamilton-Jacobi-Bellman (HJB) equation. Finally, a complete characterization of all NEs for MFGs is established by the strong duality between the linear program and its dual problem. This strong duality is obtained by the solvability of the dual problem, and in particular through the regularity of the associated HJB equation.

A key new insight of our analysis for MFGs is that the dual variable within the primal-dual formulation is only required to coincide with the solution of the HJB equation on the support of the mean field flow, reminiscent of the adjoint process in the stochastic maximum principle which only needs to be defined along the optimal state trajectory.

Compared with existing approaches for MFGs, the primal-dual formulation and its NE characterization require neither the convexity of the associated Hamiltonian nor the uniqueness of its optimizer, and remain applicable when the HJB equation lacks classical or even continuous solutions.

Venue: MCS2068

• Applied Mathematics

Usual Venue: MCS3070

Contact: andrew.krause@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Arithmetic Study Group

Usual Venue: MCS2068

Contact: herbert.gangl@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• CPT Colloquium

Usual Venue: OC218

Contact: mohamed.anber@durham.ac.uk

For more information, see HERE.

No upcoming seminars have been scheduled (not unusual outside term time).

• Department Research Colloquium

Usual Venue: MCS0001

Contact: inaki.garcia-etxebarria@durham.ac.uk,sunil.chhita@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Distinguished and Public Lectures

Usual Venue: MCS0001

Contact: sabine.boegli@durham.ac.uk,alpar.r.meszaros@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Education and Pedagogy

Usual Venue: MCS3052

Contact: andrew.krause@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Gandalf

Usual Venue: MCS3070

Contact: daniel.n.disney@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Geometry and Topology

Usual Venue: MCS2068

Contact: martin.p.kerin@durham.ac.uk

Apr 30 13:00 Anthea Monod (Imperial): TBA

Venue: MCS2068

May 07 13:00 Wilhelm Klingenberg (Durham): TBA

Venue: MCS2068

May 14 13:00 Victoria Pelayo Alvaredo (Universidad Autónoma de Madrid/ICMAT): TBA

Venue: MCS2068

• HEP Journal Club

Usual Venue: MCS3070

Contact: mendel.t.nguyen@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• HEP Lunchtime

Usual Venue: MCS0001

Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Probability

Usual Venue: MCS2068

Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Pure Maths Colloquium

Usual Venue: MCS2068

Contact: michael.r.magee@durham.ac.uk

Apr 28 15:00 Sergey Fomin (U Michigan): Incidence geometry and tiled surfaces

We show that various classical theorems of linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a general result that involves a tiling of a closed oriented surface by quadrilateral tiles. This yields a general mechanism for producing new incidence theorems and generalizing and interpreting the known ones.

This is joint work<https://arxiv.org/abs/2305.07728> with Pavlo Pylyavskyy<https://cse.umn.edu/math/pavlo-pylyavskyy>.

Venue: MCS0001

• Spectra and Moduli

Usual Venue: MCS3070

Contact: joe.thomas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Statistics

Usual Venue: MCS2068

Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Stats4Grads

Contact: adam.stone2@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).