Probability and Stochastic Analysis - University of Bonn

Teaching

Nrnamelecturer
MB05Stochastik Anton Bovier
20151   611100905   Vorlesung    SWS
Termine:
Mi 10-12Kleiner Hörsaal, Wegelerstr. 10
Mo 10-12Kleiner Hörsaal, Wegelerstr. 10
MB05Übungen zu Stochastik Anton Bovier
20151   611300905   Seminar/Übungen    SWS
Termine:
Fr 12-14SemR 0.008, Endenicher Allee 60 Gruppe 3
Di 12-14SemR 0.008, Endenicher Allee 60 Gruppe 1
Di 12-14SemR 1.007, Endenicher Allee 60 Gruppe 4, NEU!
Do 16-18SemR 0.008, Endenicher Allee 60 Gruppe 2
S1G1Seminar
20151   611100109   Seminar    SWS
Termine:
Di 10-12SemR 1.007, Endenicher Allee 60
Do 10-12N 0.008 - Neubau, Endenicher Allee 60 Vorbesprechung: Di, 24.02.15, 13:00, N0.008
Mi 12-14SemR 0.006, Endenicher Allee 60 Vorbesprechung: 24.2.15, 13.30, Raum We6, 5.002
Fr 12-14-
Do 14-16SemR 0.003, Endenicher Allee 60 Vorbesprechung: Do, 29.01.15, 16:00, Raum 4.050 EN60
Fr 14-16SemR 1.007, Endenicher Allee 60
Mo 16-18N 0.003 - Neubau, Endenicher Allee 60
S2F1Hauptseminar Stochastik Karl-Theodor Sturm
20151   611112011   Hauptseminar    SWS
Termine:
Fr 14-16SemR 0.006, Endenicher Allee 60
S2F1Hauptseminar Stochastik - Stochastische Modelle Andreas Eberle
20151   611111011   Hauptseminar    SWS
Termine:
Fr 14-16SemR 0.007, Endenicher Allee 60
S4F2Graduate Seminar on Stochastic Analysis - Interacting Particle Systems Andreas Eberle
20151   611501024   Hauptseminar    SWS
Termine:
Di 14-16N 0.007 - Neubau, Endenicher Allee 60
S5G1Master´s Thesis Seminar
20151   611500101   Seminar für Examenskandidaten    SWS
Termine:
--woech more lecturers according to prior agreement
Fr 12-14-
Do 16-17SemR 0.011, Endenicher Allee 60 appointments with examiners according to prior agreement
V1G6Algorithmische Mathematik II Martin Rumpf Anton Bovier
20151   611100106   Vorlesung    SWS
Termine:
Mo 10-12Großer Hörsaal, Wegelerstr. 10
Mi 10-12Großer Hörsaal, Wegelerstr. 10
V1G6Übungen zu Algorithmischer Mathematik II Martin Rumpf Anton Bovier
20151   611300106   Übung    SWS
Termine:
Fr 08-10SemR 0.003, Endenicher Allee 60 Gruppe 7
Fr 08-10SemR 0.007, Endenicher Allee 60 Gruppe 8
Di 10-12SemR 0.007, Endenicher Allee 60 Gruppe 1
Do 10-12SemR 0.003, Endenicher Allee 60 Gruppe 4
Do 12-14SemR 0.003, Endenicher Allee 60 Gruppe 5
Fr 12-14SemR 0.003, Endenicher Allee 60 Gruppe 9
Fr 14-16SemR 0.003, Endenicher Allee 60 Gruppe 10
Di 16-18SemR 0.007, Endenicher Allee 60 Gruppe 3
Do 16-18SemR 0.003, Endenicher Allee 60 Gruppe 6
V2F2Einführung in die Statistik Martin Huesmann
20151   611100703   Vorlesung    SWS
Termine:
Mo 12.00-14.00Großer Hörsaal, Wegelerstr. 10
Mi 12.00-14.00Großer Hörsaal, Wegelerstr. 10
V2F2Übungen zu Einführung in die Statistik Martin Huesmann
20151   611300703   Übung    SWS
Termine:
Do 14-16SemR 1.008, Endenicher Allee 60 Gruppe 2
Mi 16-18SemR 0.008, Endenicher Allee 60 Gruppe 1
Do 18-20SemR 1.008, Endenicher Allee 60 Gruppe 3
V3F1/F4F1Stochastic Processes / Stochastische Prozesse Karl-Theodor Sturm
20151   611100702   Vorlesung    SWS
Termine:
Di 08-10Kleiner Hörsaal, Wegelerstr. 10
Fr 10-12Kleiner Hörsaal, Wegelerstr. 10
V3F1/F4F1Exercises to Stochastic Processes / Übungen zu Stochastische Prozesse Karl-Theodor Sturm
20151   611300702   Übung    SWS
Termine:
Do 10-12SemR 0.008, Endenicher Allee 60
Do 12-14SemR 0.011, Endenicher Allee 60
Fr 14-16SemR 0.008, Endenicher Allee 60
Do 14-16SemR 0.008, Endenicher Allee 60
V4F1Stochastic Analysis Andreas Eberle
20151   611500701   Vorlesung    SWS
Termine:
Di 12-14Kleiner Hörsaal, Wegelerstr. 10
Do 12-14Kleiner Hörsaal, Wegelerstr. 10
V4F1Exercises to Stochastic Analysis Andreas Eberle
20151   611700701   Übung    SWS
Termine:
Mo 12-14SemR 0.011, Endenicher Allee 60
Mi 16-18SemR 0.006, Endenicher Allee 60
V5F4Selected Topics in Stochastic Analysis - Introduction to Optimal Transport and Applications Matthias Erbar
20151   611500709   Vorlesung    SWS
Termine:
Mo 08-10SemR 1.008, Endenicher Allee 60
Literatur:

References:

• C. Villani, Topics in optimal transportation

• C. Villani, Optimal transport, old and new

• L. Ambrosio, N. Gigli, A user’s guide to optimal transport

• F. Otto, The geometry of dissipative evolution equations: The porous medium equation, article

• K.-Th. Sturm, The geometry of metric measure spaces, article

Bemerkung:

The optimal transport problem has a long history dating back to Monge in the 18th century. In modern terms the problem is, given two probability distributions to find a transport map pushing one forward to the other that minimizes the total transport cost.

In the last two decades the theory has received new attention and seen an enormous development. Striking connections to a number of mathematical fields have been established ranging from probability and economics to PDE and Riemannian geometry, where optimal transport is used as a powerful and versatile tool.

In the first part of the lecture we will consider the optimal transport problem in a general setting and cover the beautiful theory leading to existence and characterization of solutions.

The second part of the lecture will give an introduction to some recent applications of optimal transport. Possible topics include:

• Otto’s geometric interpretation of evolution PDEs: Heat and porous medium equations e.g. as gradient flows in the space of probability measures, Theory of gradient flows in metric spaces

• Geometry of singular spaces: How to define a notion of Ricci curvature lower bounds for metric spaces equipped with a measure using optimal transport and properties of such spaces

• Using optimal transport to prove geometric and functional inequalities, e.g. isoperimetry and concentration

• Variants of the transport problem

 Prerequisites: A solid background in measure theory is desirable. Some basic knowledge of Riemannian geometry and PDE will be helpful but is not strictly required.