Dynamical, Symplectic and Stochastic Perspectives on Gradient-Based Optimization Michael I. Jordan University of California, Berkeley March 3, 2018

Source URL: eta.impa.br

• Numerical analysis
• Dynamical systems
• Classical mechanics
• Hamiltonian mechanics
• Symplectic integrator
• Mathematical optimization
• Gradient descent
• Leapfrog integration
• Bregman Lagrangian
• Lagrangian mechanics
• Bregman divergence

A NEW FAMILY OF SYMPLECTIC FOURFOLDS OLIVIER DEBARRE This is joint work with Claire Voisin. 1. Irreducible symplectic varieties It follows from work of Beauville and Bogomolov that any smooth

Source URL: www.math.ens.fr

• Geometry
• Algebra
• Abstract algebra
• Algebraic geometry
• Differential geometry
• Birational geometry
• Hilbert scheme
• Moduli theory
• Scheme theory
• Hodge theory
• Kodaira dimension
• Hodge structure

Proc. Int. Cong. of Math. – 2018 Rio de Janeiro, Vol–986) STABILITY CONDITIONS IN SYMPLECTIC TOPOLOGY Ivan Smith

Source URL: eta.impa.br

• Topology
• Mathematics
• Algebra
• Homotopy theory
• Symplectic topology
• Algebraic geometry
• Algebraic topology
• Geometric topology
• Algebraic K-theory
• Cohomology
• Mapping class group
• Rational homotopy theory

Week 4 (due April 30) Reading: Srednicky, sections 69, 70. See also a book by Howard Georgi, ”Lie algebras in particle physics”. 1. (a) (10 points) The complex symplectic group Sp(2N, C) is a complex subgroup of GL(2

Source URL: www.theory.caltech.edu

K3 CATEGORIES, ONE-CYCLES ON CUBIC FOURFOLDS, AND THE BEAUVILLE–VOISIN FILTRATION JUNLIANG SHEN AND QIZHENG YIN Abstract. We explore the connection between K3 categories and 0cycles on holomorphic symplectic varieties.

Source URL: bicmr.pku.edu.cn

Mathematical Research Letters 2, 119–FOUR-MANIFOLDS WITHOUT SYMPLECTIC STRUCTURES BUT WITH NONTRIVIAL

Source URL: 129.187.111.185

THE GEL’FAND-KALININ-FUKS CLASS AND CHARACTERISTIC CLASSES OF TRANSVERSELY SYMPLECTIC FOLIATIONS D. KOTSCHICK AND S. MORITA Abstract. In the early 1970’s, Gel’fand, Kalinin and Fuks [7] found an exotic characterist

Source URL: 129.187.111.185

Contemporary Mathematics Volume 542, 2011 Contact pairs and locally conformally symplectic structures G. Bande and D. Kotschick Abstract. We discuss a correspondence between certain contact pairs on the

Source URL: 129.187.111.185

SYMPLECTIC NON-SQUEEZING OF THE KDV FLOW J. COLLIANDER, M. KEEL, G. STAFFILANI, H. TAKAOKA, AND T. TAO Abstract. We prove two finite dimensional approximation results and a symplectic non-squeezing property for the Korte

Source URL: math.umn.edu

407 Documenta Math. A Symplectic Approach to Van Den Ban’s Convexity Theorem

Source URL: documenta.sagemath.org