Probabilistic Methods in Negative Curvature ORGANIZERS :Riddhipratim Basu, Anish Ghosh and Mahan Mj DATE & TIME :11 March 2019 to 22 March 2019 VENUE :Madhava Lecture Hall, ICTS, Bangalore The focal area of the program lies at the juncture of three areas: Probability theory of random walks, Ergodic theory of flows on negatively curved spaces, Gromov hyperbolic groups. Random walks on finite and infinite, finitely generated groups is a topic of considerable vintage. It is well-known, starting with Kesten's characterization of amenability, that asymptotic properties of such random walks are intimately connected to the large scale geometry of the underlying group. Vershik and Kaimanovich (1983) introduced entropic techniques to study the Poisson boundary of random walks on countable discrete groups, which is a natural measure theoretic space "at infinity" associated with the random walk. In a seminal paper in 2000, Kaimanovich gave a very general sufficient condition on the one step distribution of the walk on a hyperbolic group for the Poisson boundary to equal the (geometric) Gromov boundary. Further probabilistic methods have started being applied to hyperbolic groups relatively recently including a local limit theorem and some foundational results have been proven by the French school. From the ergodic theory perspective, one of the highlights has been the classification of stationary measures on homogeneous spaces by Benoist and Quint. The ideas in their work, in particular "exponential drift" have found applications in the seminal work of Eskin and Mirzakhani on rigidity properties on moduli spaces. This will be one of the main themes of the ergodic theory component of the workshop. The program will have 6 mini-courses of 4 lectures each, with each lecture about 1 hour 15 minutes with tentative themes as follows: 1) Dmitry Dolgopyat (University of Maryland) - Circle rotations and dynamics on the modular surface 2) Sebastien Gouezel (University of Nantes ) - Random walks on hyperbolic groups - II 3) Peter Haissinsky (Aix-Marseille University) - Random walks on hyperbolic groups - I 4) Vadim Kaimanovich (University of Ottawa) - Poisson boundaries 5) Jean-Francois Quint (Institute of Mathematics of Bordeaux) - Random walks on reductive groups 6) Francois Ledrappier (University of Notre Dame) Eligibility Criteria: The program is aimed at active researchers working in probability, ergodic theory and hyperbolic geometry with an emphasis on their interactions. One purpose of the program is to serve to bring members of the academic community (esp. the Indian community) in these areas together to foster cross-fertilization. Since the program is relatively advanced, the primary focus will be on young faculty members and postdocs in these areas. However, PhD students with demonstrable expertise in these areas are also encouraged to apply. APPLICATION DEADLINE 15 November 2018 CONTACT US pmnc2019 ictsresin

Big Bang, Black Holes & Gravitational Waves

Discussion Meeting Quantum Fields, Geometry and Representation Theory 16 July 2018 to 27 July 2018 Madhava Lecture Hall, ICTS, Bangalore The power of symmetries lies at the heart of interaction between modern mathematics and theoretical

URL : https://www.icts.res.in/discussion-meeting/vishu2017

Program School on Cluster Algebras ORGANIZERS Ashish Gupta and Ashish K Srivastava DATE & TIME 08 December 2018 to 22 December 2018 VENUE Madhava Lecture Hall, ICTS Bangalore

PROGRAM Smooth and Homogeneous Dynamics 23 September 2019 to 04 October 2019 Ramanujan Lecture Hall, ICTS Bangalore

Discussion Meeting Sphere Packing 31 October 2019 to 06 November 2019 Madhava Lecture Hall, ICTS Bangalore

Statistical Physics Methods in Machine Learning DATE : 26 December 2017 to 30 December 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the "thermodynamic" limit of large number of variables. Methods from statistical physics (eg various mean-field approaches) simplify the performance analysis of these algorithms in the limit of many variables. In particular, phase-transition like phenomena appear where the performance can undergo a discontinuous change as an underlying parameter is continuously varied. A provocative question to be explored at the meeting is whether these methods can shed theoretical light into the workings of deep networks for machine learning. The Discussion Meeting will aim to facilitate interaction between theoretical computer scientists, statistical physicists, machine learning researchers and mathematicians interested in these questions. Examples of specific topics to be covered include (but are not limited to) problems such as phase transitions in optimization and learning algorithms, matrix approximation, mixing in large networks, sub-linear time algorithms, learning theory and non convex optimization. The meeting will allow structured and and unstructured interactions among the participants around the main theme. *Participation is by invitation only. CONTACT US spmml2017 ictsresin PROGRAM LINK https://www.icts.res.in/discussion-meeting/SPMML2017