Proceedings of the International Congress of Mathematicians Seoul 2014 Vol.II
1. Logic and Foundations
Zoé Chatzidakis
Model theory of difference fields and applications to algebraic dynamics 1
Ilijas Farah
Logic and operator algebras 15
John Goodrick, Byunghan Kim, and Alexei Kolesnikov
Amalgamation functors and homology groups in model theory 41
François Loeser
Definability in non-archimedean geometry 59
Antonio Montalbán
Computability theoretic classifications for classes of structures 79
Sławomir Solecki
Recent developments in finite Ramsey theory: foundational aspects and
connections with dynamics 103
2. Algebra
Nicolás Andruskiewitsch
On finite-dimensional Hopf algebras 117
Guillermo Cortiñas
Excision, descent, and singularity in algebraic K-theory 143
Robert Guralnick
Applications of the classification of finite simple groups 163
Seok-Jin Kang
Higher representation theory and quantum affine Schur-Weyl duality 179
Martin Kassabov
Finitely Generated Groups with Controlled Pro-algebraic Completions 203
Olga Kharlampovich and Alexei Myasnikov
Model theory and algebraic geometry in groups, non-standard actions and
algorithmic problems 223
Andrei S. Rapinchuk
Towards the eigenvalue rigidity of Zariski-dense subgroups 247
Karen E. Smith
Local and global Frobenius splitting 271
3. Number Theory
Francis Brown
Motivic periods and P1n{0; 1;1} 295
Matthew Emerton
Completed cohomology and the p-adic Langlands program 319
Wee Teck Gan
Theta correspondence: recent progress and applications 343
Michael Harris
Automorphic Galois representations and the cohomology of
Shimura varieties 367
Harald Andrés Helfgott
The ternary Goldbach problem 391
D. A. Goldston, J. Pintz, and C. Y. Yıldırım
Small gaps between primes 419
Zeev Rudnick
Some problems in analytic number theory for polynomials
over a finite field 443
Peter Scholze
Perfectoid spaces and their applications 461
J.-L. Waldspurger
Stabilisation de la partie géométrique de la formule des traces tordue 487
Trevor D. Wooley
Translation invariance, exponential sums, and Waring’s problem 505
Umberto Zannier
Elementary integration of differentials in families and
conjectures of Pink 531
Yitang Zhang
Small gaps between primes and primes in arithmetic progressions
to large moduli 557
Tamar Ziegler
Linear equations in primes and dynamics of nilmanifolds 569
4. Algebraic and Complex Geometry
Kai Behrend
On the virtual fundamental class 591
Ionuţ Ciocan-Fontanine and Bumsig Kim
Quasimap theory 615
Alexander Kuznetsov
Semiorthogonal decompositions in algebraic geometry 635
Davesh Maulik
K3 surfaces in positive characteristic 661
Mircea Mustaţă
The dimension of jet schemes of singular varieties 673
Keiji Oguiso
Some aspects of explicit birational geometry inspired by
complex dynamics 695
Mark Gross and Bernd Siebert
Local mirror symmetry in the tropics 723
Yukinobu Toda
Derived category of coherent sheaves and counting invariants 745
Bertrand Toën
Derived algebraic geometry and deformation quantization 769
Misha Verbitsky
Teichmüller spaces, ergodic theory and global Torelli theorem 793
5. Geometry
Mohammed Abouzaid
Family Floer cohomology and mirror symmetry 813
Mikhail Belolipetsky
Hyperbolic orbifolds of small volume 837
Olivier Biquard
Einstein 4-manifolds and singularities 853
Fuquan Fang
Non-negatively curved manifolds and Tits geometry 867
Nancy Hingston
Loop products, Poincaré duality, index growth and dynamics 881
Jeremy Kahn and Vladimir Markovic
The surface subgroup and the Ehrenepreis conjectures 897
Aaron Naber
The Geometry of Ricci Curvature 911
André Neves
New applications of Min-max Theory 939
Yaron Ostrover
When symplectic topology meets Banach space geometry 959
Hans Ringström
On the future stability of cosmological solutions to
Einstein’s equations with accelerated expansion 983
Natasa Sesum
Solitons in geometric evolution equations 1001
Gábor Székelyhidi
Extremal Kähler metrics 1017
Peter M. Topping
Ricci flows with unbounded curvature 1033
Stefan Wenger
Isoperimetric inequalities and asymptotic geometry 1049
Daniel T. Wise
The cubical route to understanding groups 1075
6. Topology
Joseph Ayoub
A guide to (étale) motivic sheaves 1101
Charles Rezk
Isogenies, power operations, and homotopy theory 1125
Michael Entov
Quasi-morphisms and quasi-states in symplectic topology 1147
Benson Farb
Representation stability 1173
Søren Galatius
Moduli spaces of manifolds 1197
Michael A. Hill, Michael J. Hopkins, and Douglas C. Ravenel
On the non-existence of elements of Kervaire invariant one 1219
Tao Li
Heegaard splittings of 3-manifolds 1245
John Rognes
Algebraic K-theory of strict ring spectra 1259
Thomas Schick
The topology of positive scalar curvature 1285
Constantin Teleman
Gauge theory and mirror symmetry 1309
Author Index
Proceedings of the International Congress of Mathematicians Seoul 2014 Vol.III
7. Lie Theory and Generalizations
Konstantin Ardakov
ÒD-modules on rigid analytic spaces 1
Yves Benoist
Recurrence on the space of lattices 11
Emmanuel Breuillard
Diophantine geometry and uniform growth of finite and infinite groups 27
Jonathan Brundan
Schur-Weyl duality and categorification 51
Uri Bader and Alex Furman
Boundaries, rigidity of representations, and Lyapunov exponents 71
Alexander Kleshchev
Modular representation theory of symmetric groups 97
Victor Ostrik
Multi-fusion categories of Harish-Chandra bimodules 121
Bertrand Rémy
On some recent developments in the theory of buildings 143
Nicolas Ressayre
Some qualitative properties of branching multiplicities 165
Michela Varagnolo and Eric Vasserot
Double affine Hecke algebras and Hecke algebras associated with quivers 191
8. Analysis and its Applications
László Erdős
Random matrices, log-gases and Hölder regularity 213
Alessio Figalli
Quantitative stability results for the Brunn-Minkowski inequality 237
Kengo Hirachi
Q and Q-prime curvature in CR geometry 257
Tuomas Hytönen
Advances in weighted norm inequalities 279
Nets Hawk Katz
The flecnode polynomial: a central object in incidence geometry 303
Izabella Łaba
Harmonic analysis and the geometry of fractals 315
Chang-Shou Lin
Mean field equations, hyperelliptic curves and modular forms 331
Andrea Malchiodi
Liouville equations from a variational point of view 345
Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava
Ramanujan graphs and the solution of the Kadison–Singer problem 363
Jill Pipher
Carleson measures and elliptic boundary value problems 387
Tom Sanders
Roth’s theorem: an application of approximate groups 401
Wilhelm Schlag
Semilinear wave equations 425
Sasha Sodin
Several applications of the moment method in random matrix theory 451
Roland Speicher
Free probability and random matrices 477
László Székelyhidi Jr.
The h-principle and turbulence 503
9. Dynamical Systems and Ordinary Differential Equations
Viviane Baladi
Linear response, or else 525
Luigi Chierchia and Gabriella Pinzari
Metric stability of the planetary N-body problem 547
Sylvain Crovisier
Dynamics of C1-diffeomorphisms: global description and prospects for
classification 571
Albert Fathi
Weak KAM Theory: the connection between Aubry-Mather theory and
viscosity solutions of the Hamilton-Jacobi equation 597
Jens Marklof
The low-density limit of the Lorentz gas: periodic, aperiodic and random 623
Carlos Gustavo T. de A. Moreira
Fractal geometry and dynamical bifurcations 647
Mark Pollicott
Zeta functions for Anosov flows 661
Frédéric Faure and Masato Tsujii
Resonances for geodesic flows on negatively curved manifolds 683
Weixiao Shen and Sebastian van Strien
Recent developments in interval dynamics 699
10. Partial Differential Equations
Thierry Bodineau, Isabelle Gallagher, and Laure Saint-Raymond
From molecular dynamics to kinetic theory and hydrodynamics 721
Mihalis Dafermos
The mathematical analysis of black holes in general relativity 747
Panagiota Daskalopoulos
Ancient solutions to geometric flows 773
Robert L. Jerrard
Quantized vortex filaments in complex scalar fields 789
Ki-Ahm Lee
Homogenization theory in nonlinear partial differential equations 811
Robert J. McCann
Academic wages, singularities, phase transitions and pyramid schemes 835
Pierre Raphaël
On singularity formation in Hamiltonian evolution equations 849
Luis Silvestre
Regularity estimates for parabolic integro-differential equations
and applications 873
Sergiu Klainerman, Igor Rodnianski, and Jérémie Szeftel
The resolution of the bounded L2 curvature conjecture
in general relativity 895
András Vasy
Some recent advances in microlocal analysis 915
Juncheng Wei
Geometric approaches to semilinear elliptic equations 941
Shih-Hsien Yu
Duality in Boltzmann equation and its applications 965
11. Mathematical Physics
Anton Alekseev
Three lives of the Gelfand-Zeitlin integrable system 983
Ivan Corwin
Macdonald processes, quantum integrable systems and
the Kardar-Parisi-Zhang universality class 1007
Bertrand Duplantier
Liouville Quantum Gravity, KPZ and Schramm-Loewner Evolution 1035
Bertrand Eynard
An overview of the topological recursion 1063
Vladimir V. Fock
Cluster varieties and integrable systems 1087
Anton A. Gerasimov
Archimedean Langlands duality and exactly solvable quantum systems 1097
Seung-Yeal Ha
Lyapunov functional approach and collective dynamics of some interacting
many-body systems 1123
Rinat Kedem
Fermionic spectra in integrable models 1141
Sandrine Péché
Deformed ensembles of random matrices 1159
Robert Seiringer
Structure of the excitation spectrum for many-body quantum systems 1175
Samson L. Shatashvili
Gauge theory angle at quantum integrability 1195
Jörg Teschner
Quantization of moduli spaces of flat connections and Liouville theory 1223
Author Index 1247
Proceedings of the International Congress of Mathematicians Seoul 2014 Vol.IV
12 Probability and Statistics
Sourav Chatterjee
A short survey of Stein’s method 1
Geoffrey R. Grimmett
Criticality, universality, and isoradiality 25
Martin Hairer
Singular stochastic PDEs 49
Takashi Kumagai
Anomalous random walks and diffusions: From fractals to random media 75
Kenneth Lange and Kevin L. Keys
The proximal distance algorithm 95
Michel Ledoux
Heat flow, geometric and functional inequalities 117
Russell Lyons
Determinantal probability: Basic properties and conjectures 137
Terry Lyons
Rough paths, signatures and the modelling of functions on streams 163
Timo Seppäänen
Variational formulas for directed polymer and percolation models 185
Vladas Sidoravicius
Criticality and Phase Transitions: five favorite pieces 199
Alexandre B. Tsybakov
Aggregation and minimax optimality in high-dimensional estimation 225
Báint Virá
Operator limits of random matrices 247
Martin J. Wainwright
Constrained forms of statistical minimax: Computation, communication, and privacy 273
13 Combinatorics
Maria Chudnovsky
Coloring graphs with forbidden induced subgraphs 291
David Conlon
Combinatorial theorems relative to a random set 303
Jacob Fox
The graph regularity method: variants, applications, and alternative methods 329
Michael Krivelevich
Positional games 355
Daniela Kün and Deryk Osthus
Hamilton cycles in graphs and hypergraphs: an extremal perspective 381
Marc Noy
Random planar graphs and beyond 407
Grigori Olshanski
The Gelfand-Tsetlin graph and Markov processes 431
Jáos Pach
Geometric intersection patterns and the theory of topological graphs 455
Angelika Steger
The determinism of randomness and its use in combinatorics 475
Van H. Vu
Combinatorial problems in random matrix theory 489
14 Mathematical Aspects of Computer Sciences
Boaz Barak and David Steurer
Sum-of-squares proofs and the quest toward optimal algorithms 509
Mark Braverman
Interactive information and coding theory 535
Andrei A. Bulatov
Counting constraint satisfaction problems 561
Julia Chuzhoy
Flows, cuts and integral routing in graphs - an approximation algorithmist’s perspective 585
Craig Gentry
Computing on the edge of chaos: Structure and randomness in encrypted computation 609
Ryan O’Donnell
Social choice, computational complexity, Gaussian geometry, and Boolean functions 633
Ryan Williams
Algorithms for circuits and circuits for algorithms: Connecting the tractable and intractable 659
Sergey Yekhanin
Codes with local decoding procedures 683
15 Numerical Analysis and Scientific Computing
Réi Abgrall
On a class of high order schemes for hyperbolic problems 699
Annalisa Buffa
Spline differential forms 727
Yalchin Efendiev
Multiscale model reduction with generalized multiscale finite element methods 749
Chi-Wang Shu
Discontinuous Galerkin method for time-dependent convection dominated partial differential equations 767
Denis Talay
Singular stochastic computational models, stochastic analysis, PDE analysis, and numerics 787
Ya-xiang Yuan
A review on subspace methods for nonlinear optimization 807
16 Control Theory and Optimizaiton
Friedrich Eisenbrand
Recent results around the diameter of polyhedra 829
Monique Laurent
Optimization over polynomials: Selected topics 843
Adrian S. Lewis
Nonsmooth optimization: conditioning, convergence and semi-algebraic models 871
Luc Robbiano
Carleman estimates, results on control and stabilization for partial differential equations 897
Pierre Rouchon
Models and feedback stabilization of open quantum systems 921
Jiongmin Yong
Time-inconsistent optimal control problems 947
17 Mathematics in Science and Technology
Weizhu Bao
Mathematical models and numerical methods for Bose-Einstein condensation 971
Andrea Braides
Discrete-to-continuum variational methods for Lattice systems 997
Eric Cancè
Mathematical models and numerical methods for electronic structure Calculation 1017
Anna C. Gilbert
Sparse analysis 1043
Miguel Colom, Gabriele Facciolo,Marc Lebrun, Nicola Pierazzo, Martin Rais,
Yi-Qing Wang, and Jean-Michel Morel
A mathematical perspective of image denoising 1061
Barbara Niethammer
Scaling in kinetic mean-field models for coarsening phenomena 1087
Hinke M. Osinga
Computing global invariant manifolds: Techniques and applications 1101
B. Daya Reddy
Numerical approximation of variational inequalities arising in elastoplasticity 1125
Andrew M. Stuart
Uncertainty quantification in Bayesian inversion 1145
Thaleia Zariphopoulou
Stochastic modeling and methods in optimal portfolio construction 1163
18 Mathematics Education and Popularization of Mathematics
Éienne Ghys
The internet and the popularization of mathematics 1187
Güter M. Ziegler and Andreas Loos
Teaching and learning “What is Mathematics” 1203
19 History of Mathematics
Qi Han
Knowledge and power: A social history of the transmission of mathematics 1217
between China and Europe during the Kangxi reign (1662-1722)
Reinhard Siegmund-Schultze
One hundred years after the Great War (1914–014): A century of
breakdowns, resumptions and fundamental changes in international
mathematical communication 1231
Dominique Tournè
Mathematics of engineers: Elements for a new history of numerical analysis 1255
Author Index. 1275
Proceedings of the International Congress of Mathematicians Seoul 2014 Vol.I
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II-IV권의 내용은 2014 세계수학자대회에 강연했던 178편의 논문과 초청강연 모음집입니다.
