André Neves   (University of Chicago) 

29.05.2024, 17:10  (Wednesday) Zoom session

Title: Abundance of minimal hypersurfaces

Abstract:

Minimal surfaces are physical objects which appear naturally in math and applied science. In the 80’s Yau conjectured that any closed Riemannian manifold should have an infinite number of closed minimal hypersurfaces. For 30 years little progress was made but over the last 10 years a renewed interest on the problem led to its complete solution. I will survey the results, the new ingredients, and the current state of the art.

Leonard M. Blumenthal Lectures in Geometry is a distinguished lecture series delivered each academic year at School of Mathematical Sciences, Tel Aviv University. Former speakers include

Helmut Hofer,  Aleksey Pogorelov, Gilles Pisier, Marcel Berger as well as

2002-2003 Viktor L. Ginzburg (UC Santa Cruz) Periodic orbits of Hamiltonian systems:

twisted geodesic flows and relative symplectic invariants-I,II

2003-2004  Alexander Givental (UC Berkeley)  Symmetries of Gromov-Witten Theory-I,II

 2004-2005 Dmitri Burago (Penn State) Choosing "good" coordinates: from asymptotic geometry of tori to boundary rigidity-I.II

 2005-2006 Shmuel Weinberger (U. Chicago)

I. Using the telescope as a microscope: Large scale determination of small scale structure

II. Novikov conjectures and Novikov theorems

 2006-2007  Michael Kapovich (University of California, Davis)

I. Products of matrices

II. How to compute triangle inequalities

 2007-2008  Albert Fathi (ENS-Lyon)  ( abstracts)  

I. On smooth critical subsolutions of the Hamilton-Jacobi equation

II. Hamilton-Jacobi and Denjoy-Schwartz: why dynamics matters

in the regularity of smooth subsolutions?

 2007-2008 Shlomo Sternberg (Harvard)

A report on recent work of Alekseev, Bursztyn and Meinrenken

I. The symplectic category and the split orthogonal category 

II. The Alekseev, Bursztyn, Meinrenken category

III. Dirac structures and Dirac morphisms

 2009 Yakov Eliashberg (Stanford)

 I. Construction and application of maps with simple singularities

 II. Symplectic topology of Stein manifolds

 For the abstracts click here

 2011 Helmut Hofer (IAS, Princeton)

I. Symplectic Dynamics

II. Generalizations of Fredholm theory. 

For the abstracts click here

 2012 Paul Biran (ETH, Zurich)

Lagrangian topology: geometry, algebra and bureaucracy

I. Old and new invariants of Lagrangian manifolds and what to do with them

II. Geometric and algebraic aspects of Lagrangian topology

and organizational matters

Abstracts of  Blumenthal Lectures 2012

 2013 Danny Calegari (University of Chicago) 

Surfaces from linear programming

Abstract of Blumenthal Lectures 2013                   

 2014  Nicolai Reshetikhin  (UC Berkeley)  

I.  Deterministic limit shapes in statistical mechanics  

II.   Ice and 6-vertex models in statistical mechanics: mathematical perspective 

Abstract of Blumenthal Lectures 2014 

 2015  Richard Evan Schwartz (Brown University)

I. The projective heat map

II. The plaid model 

Abstracts of Blumenthal Lectures 2015  

2016   Bo Berndtsson  (Chalmers University of Technology)

Complex Brunn-Minkowski Theory 

Abstracts of the Blumenthal lectures 2016 

2017  Yair Minsky  (Yale University)

Gluing hyperbolic 3-manifolds

Abstracts of the Blumenthal Lectures 2017

2018  Peter Ozsvath (Princeton University)

Knot Floer Homology

Abstracts of Blumenthal Lectures 2018        

2019 Gang Tian (Peking University, Princeton University)

I. Analytic minimal model program

II. Recent progress on Kahler-Ricci flow

Abstracts of Blumenthal Lectures 2019    

2019-2020 Sergei Tabachnikov (Penn State University) 

I, Four equivalent properties of integrable billiards

II. Introducing symplectic billiards

Abstracts  of Blumenthal Lectures 2019-2020 

2022-2023 Grigory Mikhalkin (University of Geneva) 

I. Toric geometry and tropical trigonometry

II. Tropical, real, and symplectic geometry 

Abstracts  of Blumenthal Lectures 2022-2023