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Algèbre, Analyse, Géométrie et Physique

English title Algebra, Analysis, Geometry and Physics
Applicant Smirnov Stanislav
Number 159581
Funding scheme Project funding (Div. I-III)
Research institution Section de Mathématiques Université de Genève
Institution of higher education University of Geneva - GE
Main discipline Mathematics
Start/End 01.10.2015 - 30.09.2018
Approved amount 1'000'000.00
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All Disciplines (2)

Discipline
Mathematics
Theoretical Physics

Keywords (7)

algebra; geometry; probability; algebraic geometry; analysis; statistical mechanics; topology

Lay Summary (French)

Lead
Cet important projet interdisciplinaire finance les activités de recherche du département de mathématiques de l'université de Genève ainsi que ses collaborations avec les universités suisses environnantes.
Lay summary

Cet important projet interdisciplinaire finance les activités de recherche du département de mathématiques de l'université de Genève ainsi que ses collaborations avec les universités suisses environnantes.

Le projet s'articule autour de quatre grands axes de recherche et leurs interactions. Le premier s'intéresse aux différents aspects des problèmes de modules et leurs interactions avec les autres sujets tels que la théorie de Lie et la cohomologie équivariante. La deuxième partie se concentre sur les connections entre différents champs aussi bien classiques qu'émergents en géométrie et en topologie. La troisième partie étudie les modèles probabilistes dans les espaces euclidiens et sur les groupes. La quatrième partie étudie la théorie géométrique des groupes et les problèmes reliés aux théories ergodique et des systèmes dynamiques.

Le projet est basé sur un programme important de visites de courte et de longue durée, et finance plusieurs groupes de recherche interagissant entre eux, ainsi que plusieurs séminaires réguliers. Il contribue également à l'organisation de conférences, de workshops et d'écoles destinées aux étudiants en doctorat ainsi qu'aux chercheurs des universités de Genève et de la région. Finalement, le projet permet de financer certains trajets des membres du groupe.

 

Direct link to Lay Summary Last update: 07.09.2015

Responsible applicant and co-applicants

Publications

Publication
Potts Models with a Defect Line
Ott Sébastien, Velenik Yvan (2018), Potts Models with a Defect Line, in Communications in Mathematical Physics, 362(1), 55-106.
Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino
Alekseev Anton, Shatashvili Samson L. (2018), Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino, in Reviews in Mathematical Physics, 30(06), 1840001-1840001.
Dimers in Piecewise Temperleyan Domains
Russkikh Marianna (2018), Dimers in Piecewise Temperleyan Domains, in Communications in Mathematical Physics, 359(1), 189-222.
Spectra of Schreier graphs of Grigorchuk’s group and Schroedinger operators with aperiodic order
Grigorchuk Rostislav, Lenz Daniel, Nagnibeda Tatiana (2018), Spectra of Schreier graphs of Grigorchuk’s group and Schroedinger operators with aperiodic order, in Mathematische Annalen, 370(3-4), 1607-1637.
Chern–Simons, Wess–Zumino and other cocycles from Kashiwara–Vergne and associators
Alekseev Anton, Naef Florian, Xu Xiaomeng, Zhu Chenchang (2018), Chern–Simons, Wess–Zumino and other cocycles from Kashiwara–Vergne and associators, in Letters in Mathematical Physics, 108(3), 757-778.
Vanishing simplicial volume for certain affine manifolds
Bucher Michelle, Connell Chris, Lafont Jean-François (2018), Vanishing simplicial volume for certain affine manifolds, in Proceedings of the American Mathematical Society, 146(3), 1287-1294.
Dyson Ferrari–Spohn diffusions and ordered walks under area tilts
Ioffe Dmitry, Velenik Yvan, Wachtel Vitali (2018), Dyson Ferrari–Spohn diffusions and ordered walks under area tilts, in Probability Theory and Related Fields, 170(1-2), 11-47.
Holomorphic anomaly and quantum mechanics
Codesido Santiago, Mariño Marcos (2018), Holomorphic anomaly and quantum mechanics, in Journal of Physics A: Mathematical and Theoretical, 51(5), 055402-055402.
The Goldman–Turaev Lie bialgebra in genus zero and the Kashiwara–Vergne problem
Alekseev Anton, Kawazumi Nariya, Kuno Yusuke, Naef Florian (2018), The Goldman–Turaev Lie bialgebra in genus zero and the Kashiwara–Vergne problem, in Advances in Mathematics, 326, 1-53.
A Burau-Alexander 2-functor on tangles
Cimasoni David, Conway Anthony (2018), A Burau-Alexander 2-functor on tangles, in Fund. Math., 240(1), 51-79.
A new computation of the critical point for the planar random-cluster model with q ≥ 1
Duminil-Copin Hugo, Raoufi Aran, Tassion Vincent, others (2018), A new computation of the critical point for the planar random-cluster model with q ≥ 1, in Annales de l'Institut Henri Poincar{é}, Probabilit{é}s et Statistiques, 54(1), 422-436.
A Pfaffian formula for the monomer-dimer model on surface graphs
Pham Anh Minh (2018), A Pfaffian formula for the monomer-dimer model on surface graphs, in Lett. Math. Phys., 108(8), 1885-1904.
Alternating arm exponents for the critical planar Ising model
Wu Hao (2018), Alternating arm exponents for the critical planar Ising model, in Ann. Probab., 46(5), 2863-2907.
An explicit computation of the Blanchfield pairing for arbitrary links
Conway Anthony (2018), An explicit computation of the Blanchfield pairing for arbitrary links, in Canad. J. Math., 70(5), 983-1007.
Burau maps and twisted Alexander polynomials
Conway Anthony (2018), Burau maps and twisted Alexander polynomials, in Proc. Edinb. Math. Soc. (2), 61(2), 479-497.
Coloured tangles and signatures
Cimasoni David, Conway Anthony (2018), Coloured tangles and signatures, in Math. Proc. Cambridge Philos. Soc., 164(3), 493-530.
Conformal blocks, q-combinatorics, and quantum group symmetry
Karrila Alex, Kytölä Kalle, Peltola Eveliina (2018), Conformal blocks, q-combinatorics, and quantum group symmetry, in Ann. Inst. Henri Poincar{é} D, to appear.
Higher order corrections for anisotropic bootstrap percolation
Duminil-Copin Hugo, van Enter Aernout CD, Hulshof Tim (2018), Higher order corrections for anisotropic bootstrap percolation, in Probability Theory and Related Fields, 172(1-2), 191-243.
L2 -Burau maps and L2 -Alexander torsions
Ben Aribi Fathi, Conway Anthony (2018), L2 -Burau maps and L2 -Alexander torsions, in Osaka J. Math., 55(3), 529-545.
Low temperature interfaces: Prewetting, layering, faceting and Ferrari-Spohn diffusions
IoffeDmitry, VelenikYvan (2018), Low temperature interfaces: Prewetting, layering, faceting and Ferrari-Spohn diffusions, in Mark. Proc. Rel. Fields, 24, 487-537.
Nonexistence of torically maximal hypersurfaces
Brugallé E., Mikhalkin G., Risler J.-J., Shaw K. (2018), Nonexistence of torically maximal hypersurfaces, in Algebra i Analiz, 30(1), 20-31.
On the uniqueness of global multiple $\mathrm{SLE}$s
Beffara Vincent, Peltola Eveliina, Wu Hao (2018), On the uniqueness of global multiple $\mathrm{SLE}$s, in Mathematical Physics (math-ph).
Polychromatic arm exponents for the critical planar {FK}-Ising model
Wu Hao (2018), Polychromatic arm exponents for the critical planar {FK}-Ising model, in J. Stat. Phys., 170(6), 1177-1196.
Rational quintics in the real plane
Itenberg Ilia, Mikhalkin Grigory, Rau Johannes (2018), Rational quintics in the real plane, in Trans. Amer. Math. Soc., 370(1), 131-196.
Spectral equations for the modular oscillator
Kashaev Rinat M., Sergeev Sergey M. (2018), Spectral equations for the modular oscillator, in Rev. Math. Phys., 30(7), 1840009-28.
Spectral equations for the modular oscillator
Kashaev Rinat M., Sergeev Sergey M. (2018), Spectral equations for the modular oscillator, World Sci. Publ., Hackensack, NJ, New Jersey, 265-292.
Statistical mechanics of lattice systems
FriedliS., VelenikY. (2018), Statistical mechanics of lattice systems, Cambridge University Press, Cambridge, xix-622.
The Bethe ansatz for the six-vertex and XXZ models: An exposition
Duminil-Copin Hugo, Gagnebin Maxime, Harel Matan, Manolescu Ioan, Tassion Vincent, others (2018), The Bethe ansatz for the six-vertex and XXZ models: An exposition, in Probability Surveys, 15, 102-130.
The box-crossing property for critical two-dimensional oriented percolation
Duminil-Copin Hugo, Tassion Vincent, Teixeira Augusto (2018), The box-crossing property for critical two-dimensional oriented percolation, in Probability Theory and Related Fields, 171(3-4), 685-708.
Tropical limit of logarithmic inflection points
Mikhalkin G. B., Renodino A. (2018), Tropical limit of logarithmic inflection points, in Mat. Sb., 209(9), 19-34.
Universality for the random-cluster model on isoradial graphs
Duminil-Copin Hugo, Li Jhih-Huang, Manolescu Ioan, others (2018), Universality for the random-cluster model on isoradial graphs, in Electronic Journal of Probability, 23(96), 1-70.
Ends of Schreier graphs and cut-points of limit spaces of self-similar groups
Bondarenko Ievgen, D'Angeli Daniele, Nagnibeda Tatiana (2017), Ends of Schreier graphs and cut-points of limit spaces of self-similar groups, in Journal of Fractal Geometry, 4(4), 369-424.
Spectral zeta functions of graphs and the Riemann zeta function in the critical strip
Friedli Fabien, Karlsson Anders (2017), Spectral zeta functions of graphs and the Riemann zeta function in the critical strip, in Tohoku Mathematical Journal, 69(4), 585-610.
Goldman–Turaev formality from the Knizhnik–Zamolodchikov connection
Alekseev Anton, Naef Florian (2017), Goldman–Turaev formality from the Knizhnik–Zamolodchikov connection, in Comptes Rendus Mathematique, 355(11), 1138-1147.
The Horn problem and planar networks
Alekseev Anton, Podkopaeva Masha, Szenes Andras (2017), The Horn problem and planar networks, in Advances in Mathematics, 318, 678-710.
Œ[Q,R] = 0 and Kostant partition functions
Szenes András, Vergne Michèle (2017), Œ[Q,R] = 0 and Kostant partition functions, in L’Enseignement Mathématique, 63(3), 471-516.
Asymptotics for the determinant of the combinatorial Laplacian on hypercubic lattices
Louis Justine (2017), Asymptotics for the determinant of the combinatorial Laplacian on hypercubic lattices, in European Journal of Combinatorics, 63, 176-196.
Resurgence matches quantization
Couso-Santamaría Ricardo, Mariño Marcos, Schiappa Ricardo (2017), Resurgence matches quantization, in Journal of Physics A: Mathematical and Theoretical, 50(14), 145402-145402.
Spectral Theory and Mirror Curves of Higher Genus
Codesido Santiago, Grassi Alba, Mariño Marcos (2017), Spectral Theory and Mirror Curves of Higher Genus, in Annales Henri Poincaré, 18(2), 559-622.
Operators and higher genus mirror curves
Codesido Santiago, Gu Jie, Mariño Marcos (2017), Operators and higher genus mirror curves, in Journal of High Energy Physics, 2017(2), 92-92.
Higher genus Kashiwara–Vergne problems and the Goldman–Turaev Lie bialgebra
Alekseev Anton, Kawazumi Nariya, Kuno Yusuke, Naef Florian (2017), Higher genus Kashiwara–Vergne problems and the Goldman–Turaev Lie bialgebra, in Comptes Rendus Mathematique, 355(2), 123-127.
Spanning trees in directed circulant graphs and cycle power graphs
Louis Justine (2017), Spanning trees in directed circulant graphs and cycle power graphs, in Monatshefte für Mathematik, 182(1), 51-63.
A living mesoscopic cellular automaton made of skin scales
Manukyan Liana, Montandon Sophie A, Fofonjka Anamarija, Smirnov Stanislav, Milinkovitch Michel C (2017), A living mesoscopic cellular automaton made of skin scales, in Nature, 544(7649), 173-173.
A meromorphic extension of the 3D Index
Garoufalidis Stavros, Kashaev Rinat (2017), A meromorphic extension of the 3D Index, Research in the Mathematical Sciences, x.
A proof of the subadditive ergodic theorem
KarlssonAnders (2017), A proof of the subadditive ergodic theorem, Cambridge University Press, Cambridge, 343-354.
Amoebas of half-dimensional varieties
Mikhalkin Grigory (2017), Amoebas of half-dimensional varieties, Birkhäuser/Springer, Cham, Cham, 349-359.
Anisotropic local laws for random matrices
Knowles A., Yin. J. (2017), Anisotropic local laws for random matrices, in Prob. Theor. Rel. Fields, 169, 257-352.
Asymptotics for the determinant of the combinatorial Laplacian on hypercubic lattices
Louis Justine (2017), Asymptotics for the determinant of the combinatorial Laplacian on hypercubic lattices, in European Journal of Combinatorics, 63, 176-196.
Boundary arm exponents for {SLE}
Wu Hao, Zhan Dapeng (2017), Boundary arm exponents for {SLE}, in Electron. J. Probab., 22, 89-26.
Boundary correlations in planar {LERW} and {UST}
Karrila Alex, Kytölä Kalle, Peltola Eveliina (2017), Boundary correlations in planar {LERW} and {UST}, Mathematical Physics (math-ph); Combinatorics (math.CO); Probability (math.PR), c.
Bulk eigenvalue statistics for random regular graphs
Bauerschmidt R., Huang J., Knowles A., Yau H.-T. (2017), Bulk eigenvalue statistics for random regular graphs, in Ann. Prob., 45, 3626-3663.
Continuity of the phase transition for planar random-cluster and Potts models with 1≤q≤4
Duminil-Copin Hugo, Sidoravicius Vladas, Tassion Vincent (2017), Continuity of the phase transition for planar random-cluster and Potts models with 1≤q≤4, in Communications in Mathematical Physics, 349(1), 47-107.
Exponential decay of loop lengths in the loop O (n) model with large n
Duminil-Copin Hugo, Peled Ron, Samotij Wojciech, Spinka Yinon (2017), Exponential decay of loop lengths in the loop O (n) model with large n, in Communications in Mathematical Physics, 349(3), 777-817.
From state integrals to {$q$}-series
Garoufalidis Stavros, Kashaev Rinat (2017), From state integrals to {$q$}-series, in Math. Res. Lett., 24(3), 781-801.
Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions d≤3
Fr�hlich J., Knowles A., Schlein B., Sohinger V.\ (2017), Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions d≤3, in Comm. Math. Phys., 356, 883-980.
Isotropic self-consistent equations for mean-field random matrices
He Y., Knowles A., Rosenthal R. (2017), Isotropic self-consistent equations for mean-field random matrices, in Prob. Theor. Rel. Fields, 171, 203-249.
Local semicircle law for random regular graphs
Bauerschmidt R., Knowles A., Yau H.-T. (2017), Local semicircle law for random regular graphs, in Comm. Pure Appl. Math., 70, 1898-1960.
Mesoscopic eigenvalue statistics of Wigner matrices
He Y., Knowles A. (2017), Mesoscopic eigenvalue statistics of Wigner matrices, in Ann. Appl. Prob., 27, 1510-1550.
On spectra of Koopman, groupoid and quasi-regular representations
Dudko Artem, Grigorchuk Rostislav (2017), On spectra of Koopman, groupoid and quasi-regular representations, in Journal of Modern Dynamics, 11(03), 99-123.
Quantum indices and refined enumeration of real plane curves
Mikhalkin Grigory (2017), Quantum indices and refined enumeration of real plane curves, in Acta Math., 219(1), 135-180.
Random curves, scaling limits and Loewner evolutions
Kemppainen Antti, Smirnov Stanislav (2017), Random curves, scaling limits and Loewner evolutions, in Ann. Probab., 45(2), 698-779.
Revisiting the combinatorics of the 2D Ising model
Chelkak Dmitry, Cimasoni David, Kassel Adrien (2017), Revisiting the combinatorics of the 2D Ising model, in Ann. Inst. Henri Poincaré D, 4(3), 309-385.
The sharp threshold for the Duarte model
Bollobás Béla, Duminil-Copin Hugo, Morris Robert, Smith Paul, others (2017), The sharp threshold for the Duarte model, in The Annals of Probability, 45(6b), 4222-4272.
Совместный спектр и бесконечная диэдральная группа
Григорчук Р. И., Янг Р. (2017), Совместный спектр и бесконечная диэдральная группа, in Труды математического института им. Стеклова, 297(02), 165-200.
A functional relation for L -functions of graphs equivalent to the Riemann Hypothesis for Dirichlet L -functions
Friedli Fabien (2016), A functional relation for L -functions of graphs equivalent to the Riemann Hypothesis for Dirichlet L -functions, in Journal of Number Theory, 169, 342-352.
Topological Strings from Quantum Mechanics
Grassi Alba, Hatsuda Yasuyuki, Mariño Marcos (2016), Topological Strings from Quantum Mechanics, in Annales Henri Poincaré, 17(11), 3177-3235.
Logarithms and deformation quantization
Alekseev Anton, Rossi Carlo A., Torossian Charles, Willwacher Thomas (2016), Logarithms and deformation quantization, in Inventiones mathematicae, 206(1), 1-28.
Matrix Models from Operators and Topological Strings, 2
Kashaev Rinat, Mariño Marcos, Zakany Szabolcs (2016), Matrix Models from Operators and Topological Strings, 2, in Annales Henri Poincaré, 17(10), 2741-2781.
Exact quantization conditions for cluster integrable systems
Franco Sebastián, Hatsuda Yasuyuki, Mariño Marcos (2016), Exact quantization conditions for cluster integrable systems, in Journal of Statistical Mechanics: Theory and Experiment, 2016(6), 063107-063107.
Weakly maximal subgroups in regular branch groups
Bou-Rabee Khalid, Leemann Paul-Henry, Nagnibeda Tatiana (2016), Weakly maximal subgroups in regular branch groups, in Journal of Algebra, 455, 347-357.
Exact quantization conditions for the relativistic Toda lattice
Hatsuda Yasuyuki, Mariño Marcos (2016), Exact quantization conditions for the relativistic Toda lattice, in Journal of High Energy Physics, 2016(5), 133-133.
Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra
Grigorchuk R, Leemann P-H, Nagnibeda T (2016), Lamplighter groups, de Brujin graphs, spider-web graphs and their spectra, in Journal of Physics A: Mathematical and Theoretical, 49(20), 205004-205004.
A Formula for the Energy of Circulant Graphs with Two Generators
Louis Justine (2016), A Formula for the Energy of Circulant Graphs with Two Generators, in Journal of Applied Mathematics, 2016, 1-4.
A Formula for the Energy of Circulant Graphs with Two Generators
Louis Justine (2016), A Formula for the Energy of Circulant Graphs with Two Generators, in Journal of Applied Mathematics, 2016, 1-4.
A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model
Duminil-Copin Hugo, Tassion Vincent (2016), A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model, in Communications in Mathematical Physics, 343(2), 725-745.
A new proof of the sharpness of the phase transition for Bernoulli percolation on ℤd
Duminil-Copin H., Tassion V. (2016), A new proof of the sharpness of the phase transition for Bernoulli percolation on ℤd, in Enseignement Mathématique, 62(1-2), 199-206.
A quantitative Burton--Keane estimate under strong FKG condition
Duminil-Copin Hugo, Ioffe Dmitry, Velenik Yvan, others (2016), A quantitative Burton--Keane estimate under strong FKG condition, in The Annals of Probability, 44(5), 3335-3356.
A TQFT of Turaev–Viro Type on Shaped Triangulations
Kashaev Rinat, Luo Feng, Vartanov Grigory (2016), A TQFT of Turaev–Viro Type on Shaped Triangulations, in Ann. Henri Poincaré, 17(5), 1109-1143.
Absence of infinite cluster for critical Bernoulli percolation on slabs
Duminil Hugo, Sidoravicius Vladas, Tassion Vincent (2016), Absence of infinite cluster for critical Bernoulli percolation on slabs, in Communications on Pure and Applied Mathematics, 69(7), 1397-1411.
Combinatorics of the Teichmüller {TQFT}
Kashaev Rinat (2016), Combinatorics of the Teichmüller {TQFT}, in Winter Braids Lect. Notes, 3(Winter Bra), 2-16.
Conformal invariance of crossing probabilities for the Ising model with free boundary conditions
Benoist Stéphane, Duminil-Copin Hugo, Hongler Clément, others (2016), Conformal invariance of crossing probabilities for the Ising model with free boundary conditions, in Annales de l'Institut Henri Poincar{é}, Probabilit{é}s et Statistiques, 52(4), 1784-1798.
Crossing probabilities in topological rectangles for the critical planar FK-Ising model
Chelkak Dmitry, Duminil-Copin Hugo, Hongler Clément, others (2016), Crossing probabilities in topological rectangles for the critical planar FK-Ising model, in Electronic Journal of Probability, 21, 1-28.
Identities between dimer partition functions on different surfaces
Cimasoni David, Pham Anh Minh (2016), Identities between dimer partition functions on different surfaces, in J. Stat. Mech. Theory Exp., (10), 103101-22.
Linearization of Poisson Lie group structures
Alekseev Anton, Meinrenken Eckhard (2016), Linearization of Poisson Lie group structures, in Journal of Symplectic Geometry, 14(1), 227-267.
Link Floer homology categorifies the Conway function
Benheddi Mounir, Cimasoni David (2016), Link Floer homology categorifies the Conway function, in Proc. Edinb. Math. Soc. (2), 59(4), 813-836.
Matrix models from operators and topological strings, 2
Kashaev Rinat, Mariño Marcos, Zakany Szabolcs (2016), Matrix models from operators and topological strings, 2, in Ann. Henri Poincaré, 17(10), 2741-2781.
On the principal components of sample covariance matrices
Bloemendal A., Knowles A., Yau H.-T., Yin. J. (2016), On the principal components of sample covariance matrices, in Prob. Theor. Rel. Fields, 164, 459-552.
On the probability that self-avoiding walk ends at a given point
Duminil-Copin Hugo, Glazman Alexander, Hammond Alan, Manolescu Ioan, others (2016), On the probability that self-avoiding walk ends at a given point, in The Annals of Probability, 44(2), 955-983.
Operators from mirror curves and the quantum dilogarithm
Kashaev Rinat, Mariño Marcos (2016), Operators from mirror curves and the quantum dilogarithm, in Comm. Math. Phys., 346(3), 967-994.
Real algebraic knots and links of small degree
Mikhalkin Grigory, Orevkov Stepan (2016), Real algebraic knots and links of small degree, in J. Knot Theory Ramifications, 25(12), 1642010-34.
Splitting numbers and signatures
Cimasoni David, Conway Anthony, Zacharova Kleopatra (2016), Splitting numbers and signatures, in Proc. Amer. Math. Soc., 144(12), 5443-5455.
The phase transitions of the planar random-cluster and Potts models with q larger than 1 are sharp
Duminil-Copin Hugo, Manolescu Ioan (2016), The phase transitions of the planar random-cluster and Potts models with q larger than 1 are sharp, in Probability Theory and Related Fields, 164(3-4), 865-892.
The Yang-Baxter relation and gauge invariance
Kashaev Rinat (2016), The Yang-Baxter relation and gauge invariance, in J. Phys. A, 49(16), 164001-16.
A FORMULA FOR THE NUMBER OF SPANNING TREES IN CIRCULANT GRAPHS WITH NONFIXED GENERATORS AND DISCRETE TORI
LOUIS JUSTINE (2015), A FORMULA FOR THE NUMBER OF SPANNING TREES IN CIRCULANT GRAPHS WITH NONFIXED GENERATORS AND DISCRETE TORI, in Bulletin of the Australian Mathematical Society, 92(03), 365-373.
Heat kernels on regular graphs and generalized Ihara zeta function formulas
Chinta G., Jorgenson J., Karlsson A. (2015), Heat kernels on regular graphs and generalized Ihara zeta function formulas, in Monatshefte für Mathematik, 178(2), 171-190.
Brief introduction to tropical geometry
Brugallé Erwan, Itenberg Ilia, Mikhalkin Grigory, Shaw Kristin (2015), Brief introduction to tropical geometry, in Proceedings of the Gökova Geometry-Topology Conference 2014, 1-75, Gökova Geometry/Topology Conference (GGT), Gökova, Gökova1-75.
Disorder, entropy and harmonic functions
BenjaminiItai, Duminil-CopinHugo, KozmaGady, YadinAriel (2015), Disorder, entropy and harmonic functions, in The Annals of Probability, (5), 2332-2373.
Kac-Ward operators, Kasteleyn operators, and s-holomorphicity on arbitrary surface graphs
Cimasoni David (2015), Kac-Ward operators, Kasteleyn operators, and s-holomorphicity on arbitrary surface graphs, in Ann. Inst. Henri Poincaré D, 2(2), 113-168.
On the critical parameters of the q>4 random-cluster model on isoradial graphs
Beffara V., Duminil-Copin H., Smirnov S. (2015), On the critical parameters of the q>4 random-cluster model on isoradial graphs, in J. Phys. A, 48(48), 484003-25.
Random currents and continuity of Ising model's spontaneous magnetization
Aizenman Michael, Duminil-Copin Hugo, Sidoravicius Vladas (2015), Random currents and continuity of Ising model's spontaneous magnetization, in Communications in Mathematical Physics, 334(2), 719-742.
Seven-dimensional forest fires
Ahlberg Daniel, Duminil-Copin Hugo, Kozma Gady, Sidoravicius Vladas, others (2015), Seven-dimensional forest fires, in Annales de l'Institut Henri Poincar{é}, Probabilit{é}s et Statistiques, 51(3), 862-866.
The Altshuler-Shklovskii formulas for random band matrices {II}: the general case
Erd\Hos L., Knowles A. (2015), The Altshuler-Shklovskii formulas for random band matrices {II}: the general case, in Ann. H. Poincaré, 16, 709-799.
The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case
Erd\Hos L., Knowles A. (2015), The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case, in Comm. Math. Phys., 333, 1365-1416.
Schreier graphs of Grigorchuk's group and a subshift associated to a nonprimitive substitution
GrigorchukRostislav, LenzDaniel, NagnibedaTatiana, Schreier graphs of Grigorchuk's group and a subshift associated to a nonprimitive substitution, Cambridge Univ. Press, Cambridge, 250-299.
Subadditive and multiplicative ergodic theorem
GouezelSebastien, KarlssonAnders, Subadditive and multiplicative ergodic theorem, in J. Eur. Math.Soc, 1-20.

Collaboration

Group / person Country
Types of collaboration
Université Paris 7 France (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
ETHZ Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
- Exchange of personnel
ENS Lyon France (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
- Exchange of personnel
EPFL Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
Université Paris-Sud 11, Orsay France (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
- Exchange of personnel
Texas A&M University United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Exchange of personnel
University of Helsinki Finland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Exchange of personnel
Ecole Polytechnique France (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Princeton University United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Exchange of personnel
Oxford Great Britain and Northern Ireland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Exchange of personnel
Steklov Institute Russia (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
- Exchange of personnel
MIT United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Research Infrastructure
- Exchange of personnel
Toronto Canada (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Exchange of personnel

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Saint-Flour summer school Talk given at a conference Graphical representations of the Ising model 08.07.2018 Clermont Auvergne, France Duminil Hugo;
IST summer school in Mathematical physics Talk given at a conference Sharp threshold phenomena via randomized algorithms 04.06.2018 Klosterneuburg, Australia Duminil Hugo;
Spin Systems: Discrete and Continuous Talk given at a conference Peierls argument, random cluster, correlation inequalities 19.03.2018 Darmstadt, Germany Duminil Hugo;
Colloquium of the Department of Mathematics and Statistics Individual talk Amenability 27.02.2018 Helsinki, Russia Smirnova-Nagnibeda Tatiana;
Colloquium of the Steklov Institute Individual talk Amenability of finitely generated groups 02.11.2017 Moscow, Russia Smirnova-Nagnibeda Tatiana;
XXI Escola Brasileira de Probabilidade Talk given at a conference Sharpness results via randomized algorithms 31.07.2017 Rio de Janeiro, Brazil Duminil Hugo;
The 19th Takagi Lectures Talk given at a conference Sharp Threshold Phenomena in Statistical Physics 08.07.2017 Kyoto, Japan Duminil Hugo;
IAS Women and Mathematics Program Talk given at a conference Advanced Lecturer "Amenability" 15.05.2017 Princeton, United States of America Smirnova-Nagnibeda Tatiana;
Terry Wall Lecture Individual talk What is a ferromagnet? - The Ising model from 1920 to the present day 12.05.2017 Liverpool University, Great Britain and Northern Ireland Smirnov Stanislav;
PIMS-CRM Summer School in Probability Talk given at a conference Graphical approach to lattice spin models 06.05.2017 Vancouver, Canada Duminil Hugo;
Charles River Lectures Talk given at a conference Order - disorder operators in planar and almost planar graphs (2) 30.09.2016 Massachusetts, United States of America Duminil Hugo;
Universality, Scaling Limits and Effective Theories Talk given at a conference c 11.07.2016 Rome, Italy Duminil Hugo;
Current Developments in Mathematics Talk given at a conference Geometric approaches to lattice spin models 20.11.2015 Massachusetts, United States of America Duminil Hugo;


Awards

Title Year
Invited speaker (session Probability and session mathematical Physics), ICM Rio 2018
Gårding Prize, from the Royal Physiographical Society in Lund 2017
Grand Prix Jacques Herbrand de l'Académie des Sciences. 2017New Horizons Prize in Mathematics 2017
Loeve Prize 2017
University of Helsinki, doctor honoris causa 2017
Prize of the European Mathematical Society 2016
California Institute of Technology, distinguished alumnus 2015
Cours Peccot du collège de France 2015
Early Career Award of the International Association of Mathematical Physics 2015
Edlund Prize, from the Royal Swedish Academy of Sciences 2015

Associated projects

Number Title Start Funding scheme
178828 Algèbre, Analyse, Géométrie et Physique 01.10.2018 Project funding (Div. I-III)
162431 Low dimensional topology and quantum theory 01.01.2016 Project funding (Div. I-III)
141329 Algèbre, Analyse, Géométrie et Physique 01.10.2012 Project funding (Div. I-III)
126817 Algèbre, Analyse, Géométrie et Physique 01.10.2009 Project funding (Div. I-III)
141869 NCCR SwissMAP: The Mathematics of Physics (phase I) 01.07.2014 National Centres of Competence in Research (NCCRs)
175799 Enumerative Geometry of Hilbert schemes and Higgs moduli 01.01.2018 Project funding (Div. I-III)
182111 Topics in real algebraic geometry 01.10.2018 Project funding (Div. I-III)
141329 Algèbre, Analyse, Géométrie et Physique 01.10.2012 Project funding (Div. I-III)
178794 Linearization, Poisson structures and Quantization 01.04.2018 Project funding (Div. I-III)
169088 Non semi-simple quantum invariants 01.12.2016 Project funding (Div. I-III)

Abstract

This large multidisciplinary project supports the research activities at the Department of Mathematics of the University of Geneva during three academic years 2015-2018. It covers several research groups interacting among themselves, as well as with EPFL, ETHZ, CERN and Swiss universities.The project centers around an extensive visitor program, and supports a number of research activities. It is a natural continuation of the successful program existing for almost 40 years. Compared with the previous application, the project becomes bigger, with a new member joining our department, H. Duminil-Copin. We also have announced two new positions, and expect two new professors to join the department within the next two years. So the number of the participating professors together with postdocs and graduate students has grown to above 50, and further increase is expected during the project period.The proposed research covers several areas of modern mathematics. Below we highlighted some of the questions to be explored, collecting them into four main directions, with significant interaction among those:(1) Moduli problems and their applications (A. Alekseev and A. Szenes);(2) Geometry and topology (R. Kashaev, M. Marino and G. Mikhalkin);(3) Probability, complex analysis and statistical mechanics (D. Cimasoni, H. Duminil-Copin, S. Smirnov and Y. Velenik);(4) Groups, geometry, dynamics, probability (M. Bucher, A. Karlsson and T. Smirnova-Nagnibeda).Part (1) of this project is devoted to moduli of flat connections and moduli of Higgs bundles; symplectic, algebraic and topological aspects of moduli problems; interactions with other subjects such as Lie theory and equivariant cohomology. In this part we expect about 12 months of longer visits per year.Part (2) is about the complex Chern-Simons theory; geometrical understanding of state integral 3-manifold invariants; spectral problems and topological strings; exploring new connections between tropical and symplectic geometry. We expect about 13 months of longer visits per year.Part (3) focuses on conformal invariance and universality of the critical Ising model on biperiodic graphs; XOR-Ising model and twisted Kac-Ward matrices; universality for cellular automata; probability on groups; harmonic measure, fractals and (quasi)conformal maps; a system of mutually avoiding Ferrari-Spohn diffusions. We expect about 16 months of longer visits per year.Part (4) concerns various topics in geometric group theory and related subjects: geometry of character varieties; bounded cohomology; complexity of manifolds; spectral theory of graphs and metric spaces; measurable group theory; dynamics of group actions; probabilities on groups. We expect about 14 months of longer visits per year.The project will support about 55 months of longer visits per year for three years, as well as a number of short term visitors to present talks at our seminars and colloquium. It will contribute to organizing several conferences, workshops and schools in 2015-2018, and to travel of our team members to conferences and other universities. We also plan to partially support a few visiting professors on sabbatical, who will give advanced courses, participate in running our seminars, and actively pursue joint research projects.
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