PF 2019

December 12, 2018 from 5:00 PM at Refectory of Augustinian Abbey at Mendel Square - Mendel Museum

Robert Bryant

The Best Possible Shapes of Surfaces

Abstract:  Much of classical mathematics involves finding a configuration or shape that provides an optimum solution to a problem.  For example, it has long been known (though a rigorous proof took quite a while to find) that the surface of least area enclosing a given volume is a round sphere.  There are many other ways to measure surfaces, though, and finding 'the' surface that optimizes a given 'measurement' (subject to some given constraints) remains a challenging problem that has motivated some of the deepest recent work in the mathematics of geometric shapes.
In this talk, I will explain some of the classic ways to measure shapes of surfaces and relate this to classical problems involving surface area (soap films and bubbles) and total curvature as well to as recent progress by myself and others on these important optimization problems.

Dear Friends of Mathematics and Hikes,

You are cordially invited to the 20th mathematical hike. It will take place on December 15th 2018.

Start at 10:03 at the tram stop "Proškovo náměstí". We have planned a 13 km path - climb up Hády hill, yellow path towards Hornek and through the valley of "Říčka" to the bus stop "Mariánské údolí".

Have a nice December,

Jana Bartoňová and Jonatan Kolegar, organizers,
Jan Slovák, Director of the Department of Mathematics and Statistics

December 5, 2018 from 5:00 PM at Refectory of Augustinian Abbey at Mendel Square - Mendel Museum

Nigel Hitchin

Algebraic Geometry and Differential Equations

Abstract:

The use of elliptic functions to solve equations like the motion of a pendulum or a rigid body is a shadow of a much wider area of application of algebraic geometric notions to solving special nonlinear differential equations. The lecture will show how some natural procedures in algebraic geometry help to understand the behavior of integrable systems, especially near the so-called critical locus.

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