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Institute of Mathematics at the University of Granada (IMAG)

Soap films and bubbles have fascinated children and scientists for centuries. Mathematically, minimal surface theory -- with roots reaching back to Euler -- has been fundamental in the development of geometric analytic techniques and is presently experiencing extraordinary progress. It stands at the crossroads of several scientific disciplines including geometric analysis, algebraic geometry, dynamical systems, and mathematical physics (string theory, quantum field theories). The workshop will facilitate interactions and foster long-term collaborations between researchers in these areas who are – often unbeknownst – studying similar phenomena from different perspectives while using different techniques.

Institute of Mathematics at the University of Granada (IMAG)

Mathematical developments of the last decades indicate that geometry of high dimensions, when viewed correctly, creates remarkable order and simplicity rather than untamed complexity. Its applications permeated the fields of analysis and probability, reaching far away domains as Theoretical Computer Science and Statistical Physics while, simultaneously, methods and techniques came from a variety of directions ranging from classical analysis and probability to dynamical systems and topological methods. Recent striking results such as the near resolution of the Kannan, Lov\'asz and Simonovits (KLS) conjecture and the Bourgain slicing problem, the proof of the Gaussian Correlation Conjecture and advances in concentration of measure, make ripe the timing of this workshop on the effects of convexity and probability on high-dimensional geometric phenomena. By exploiting the scientific momentum, the workshop aims to engage a new generation in exciting collaborations and research directions.

MDPI