EXC 59:  Mathematik: Grundlagen, Modelle, Anwendungen

• Fachliche Zuordnung: Mathematik ; Informatik ; Wirtschaftswissenschaften
• Förderung: Förderung von 2006 bis 2018
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 24102279

• Erstellungsjahr: 2019

Zusammenfassung der Projektergebnisse

Das Hausdorff Center for Mathematics (HCM) nutzte die einzigartigen Möglichkeiten der Exzellenzinitiative, um in Deutschland nachhaltig ein weltweit führendes Zentrum mathematischer Spitzenforschung zu etablieren, auf Augenhöhe mit den mathematischen Fachbereichen der besten europäischen und US-amerikanischen Universitäten. Wir betreiben weltweit richtungsweisende mathematische Grundlagenforschung und entwickeln die von Wissenschaft und Gesellschaft benötigten mathematischen Methoden und Werkzeuge. Besondere Schwerpunkte unserer Forschungsagenda umfassten: Arithmetische algebraische Geometrie; Darstellungstheorie und Topologie; Geometrie, metrische Maßräume und optimaler Transport; singuläre stochastische partielle Differentialgleichungen und harmonische Analysis; mathematische Modelle von Materialien und virtuelles Material-Design; mathematische Modelle in der Immunologie; Mechanismus-Design und Spieltheorie; geometrische Bildgebung und -verarbeitung; Algorithmen, Komplexität und kombinatorische Optimierung. HCM verstärkte sein Team international herausragender Wissenschaftlerinnen und Wissenschaftler durch Rekrutierungen aus Berkeley, Oxford, Paris und Los Angeles sowie durch Abwehr von Rufen aus Chicago, Harvard, MIT, Northwestern, Oxford, Princeton und Yale. Forscher von HCM wurden mit hohen Ehrungen ausgezeichnet, wie z.B. der Fields-Medaille, 4 Leibniz-Preisen und 5 ERC Advanced Grants. Das ‘Hausdorff Research Institute for Mathematics’, 2006 als Teil von HCM gegründet, wurde zu einem führenden Institut für thematische Programme in der Mathematik. Unsere Nachwuchsprogramme mit ihrer starken Betonung auf frühe Selbstständigkeit, Gleichstellung und Inter nationalisierung wurden zu einem Eingangsportal für herausragende junge Wissenschaftler in das deutsche Universitätssystem. Die ‘Bonn International Graduate School of Mathematics’ wurde zu einer einheitlichen Ausbildungs- und Serviceeinrichtung für Doktoranden ausgebaut, und das GlobalMathNetwork befördert den internationalen Austausch von Doktoranden durch ein weltweites Netzwerk der besten Forschungszentren und Graduiertenschulen in der Mathematik. Die ‘Hausdorff School for Advanced Studies in Mathematics’ bietet ein bislang einzigartiges innovatives Trainings- und Ausbildungsprogramm für Postdoktoranden aus Deutschland und der ganzen Welt. Mit dem Programm der ‘Bonn Junior Fellows’ bieten wir exzellenten Forschern im frühen Stadium der Karriere eine temporäre W2-Professur mit ausgezeichneten Arbeitsbedingungen.

Link zum Abschlussbericht

https://dx.doi.org/10.2314/GBV:1697242545

Projektbezogene Publikationen (Auswahl)

• The stable homotopy category is rigid. Ann. of Math. (2), 166(3):837–863, 2007
  Schwede, Stefan
  
• Triangulated categories without models. Invent. Math., 170(2):231–241, 2007
  Muro, Fernando; Schwede, Stefan & Strickland, Neil
  
• Approximation algorithms for a facility location problem with service capacities. ACM Transactions of Algorithms, 4, 2008. Article 50
  Maßberg, Jens & Vygen, Jens
  
• Geometry of the mapping class groups. I. Boundary amenability. Invent. Math., 175(3):545–609, 2009
  Hamenstädt, Ursula
  
• Invariant Radon measures on measured lamination space. Invent. Math., 176(2):223–273, 2009
  Hamenstädt, Ursula
  
• On admissibility criteria for weak solutions of the Euler equations. Arch. Ration. Mech. Anal. 195(1):225–260, 2010
  de Lellis, Camillo & Székelyhidi, László
  
• Uniform energy distribution for an isoperimetric problem with long-range interactions. J. Amer. Math. Soc., 22(2):569–605, 2009
  Alberti, Giovanni; Choksi, Rustum & Otto, Felix
  
• Carleman estimates and unique continuation for second order parabolic equations with nonsmooth coefficients. Comm. Partial Differential Equations, 34(4-6):305–366, 2009
  Koch, Herbert & Tataru, Daniel
  
• Derived equivalences of K3 surfaces and orientation. Duke Math. J., 149(3):461–507, 2009
  Huybrechts, Daniel; Macrì, Emanuele & Stellari, Paolo
  
• Energy barriers and hysteresis in martensitic phase transformations. Acta Mater., 57:4332–4352, 2009
  Zhang, Zhiyong; James, Richard D. & Müller, Stefan
  
• Entropic measure and Wasserstein diffusion. Ann. Prob., 37(3):1114–1191, 2009
  von Renesse, Max-K. & Sturm, Karl-Theodor
  
• Optimized general sparse grid approximation spaces for operator equations. Mathematics of Computations, 78(268):2223–2257, 2009
  Griebel, M. & Knapek, S.
  
• Smoothing splines estimators for functional linear regression. Annals of Statistics, 37:35–72, 2009
  Crambes, Christophe; Kneip, Alois & Sarda, Pascal
  
• Spectral asymptotics for arithmetic quotients of SL(n, R)/SO(n). Duke Math. J., 149(1):117–155, 2009
  Lapid, Erez & Müller, Werner
  
• The theory of assortative matching based on costly signals. Review of Economic Studies, 76(1):253–281, 2009
  HOPPE, HEIDRUN C.; MOLDOVANU, BENNY & SELA, ANER
  
• A continuum mechanical approach to geodesics in shape space. Int. J. Comput. Vis., 93:293–318, 2011
  Wirth, Benedikt; Bar, Leah; Rumpf, Martin & Sapiro, Guillermo
  
• Coverings of p-adic period domains. J. Reine Angew. Math., 643:111–139, 2010
  Faltings, Gerd
  
• Homogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperatures. Ann. Probab., 38(2):661–713, 2010
  Bovier, Anton; den Hollander, Frank & Spitoni, Cristian
  
• Incentive problems with hidden characteristics: A unified approach. Econometrica, 78(4):1201–1237, 2010
  M. Hellwig
  
• Limit process of stationary TASEP near the characteristic line. Comm. Pure Appl. Math. 63(8):1017–1070, 2010
  Baik, Jinho; Ferrari, Patrik L. & Péché, Sandrine
  
• Noether-Lefschetz theory and the Yau-Zaslow conjecture. J. Amer. Math. Soc., 23(4):1013–1040, 2010
  Klemm, A.; Maulik, D.; Pandharipande, R. & Scheidegger, E.
  
• Special cycles on unitary Shimura varieties I. Unramified local theory. Invent. Math., 184(3):629–682, 2011
  Kudla, Stephen & Rapoport, Michael
  
• Combinatorial optimization in VLSI design. In: ”Combinatorial Optimization: Methods and Applications” (V. Chvátal, ed.), IOS Press, Amsterdam 2011, pp. 33–96
  Heidhues, Paul; Rady, Sven & Strack, Philipp
  
• Faster min-max resource sharing in theory and practice. Mathematical Programming Computation 3:1–35, 2011
  Müller, Dirk; Radke, Klaus & Vygen, Jens
  
• Generic bases for cluster algebras and the Chamber ansatz. J. Amer. Math. Soc. 25(1):21–76, 2012
  Geiß, Christof; Leclerc, Bernard & Schröer, Jan
  
• Negatively correlated bandits. Rev. Econ. Stud., 78(2):693–732, 2011
  Klein, N. & Rady, S.
  
• On the spectral side of Arthur’s trace formula — absolute convergence. Ann. of Math. (2), 174(1):173–195, 2011
  Finis, Tobias; Lapid, Erez & Müller, Werner
  
• Evaluation of the multiple zeta values ζ(2, ..., 2, 3, 2, ..., 2). Ann. of Math. (2) 175(2):977–1000, 2012
  Zagier, Don
  
• Futures cross-hedging with a stationary basis. Journal of Financial and Quantitative Analysis, 47(6):1361–1395, 2012
  Ankirchner, Stefan; Dimitroff, Georgi; Heyne, Gregor & Pigorsch, Christian
  
• Highest weight categories arising from Khovanov’s diagram algebra IV: The general linear supergroup. J. Eur. Math. Soc. (JEMS), 14(2):373–419, 2012
  Brundan, Jonathan & Stroppel, Catharina
  
• On the cohomology of compact unitary group Shimura varieties at ramified split places. J. Amer. Math. Soc. 26(1):261–294, 2013
  Scholze, Peter & Shin, Sug
  
• Perfectoid spaces. Publ. Math. Inst. Hautes Études Sci., 116:245–313, 2012
  Scholze, Peter
  
• Self-similar solutions with fat tails for Smoluchowski’s coagulation equation with locally bounded kernels. Comm. Math. Phys., 318(2):505–532, 2013
  Niethammer, B. & Velázquez, J. J. L.
  
• Sparse Legendre expansions via 1 -minimization. J. Approx. Theory 164(5):517–533, 2012
  Rauhut, Holger & Ward, Rachel
  
• The Borel conjecture for hyperbolic and CAT(0)-groups. Ann. of Math. (2), 175(2):631–689, 2012
  Bartels, Arthur & Lück, Wolfgang
  
• The extremal process of branching Brownian motion. Probab. Theory Related Fields, 157(3-4):535–574, 2013
  Arguin, Louis-Pierre; Bovier, Anton & Kistler, Nicola
  
• The Langlands-Kottwitz approach for some simple Shimura varieties. Invent. Math. 192(3): 627–661, 2013
  Scholze, Peter
  
• The Langlands-Kottwitz method and deformation spaces of p-divisible groups. J. Amer. Math. Soc. 26(1):227–259, 2013
  Scholze, Peter & Shin, Sug
  
• The local Langlands correspondence for GLn over p-adic fields. Invent. Math. 192(3):663–715, 2013
  Scholze, Peter
  
• Trading GRH for algebra: Algorithms for factoring polynomials and related structures. Mathematics of Computation, 81 (277):493–531, 2011
  Ivanyos, Gábor; Karpinski, Marek; Rónyai, Lajos & Saxena, Nitin
  
• Approximating L2 -invariants and homology growth. Geom. Funct. Anal., 23(2):622–663, 2013
  Lück, W.
  
• Approximating rough stochastic PDEs. Comm. Pure Appl. Math. 67(5):776–870, 2014
  Hairer, Martin; Maas, Jan & Weber, Hendrik
  
• Milnor invariants and twisted Whitney towers. J. Topol., 7(1):187–224, 2014
  Conant, J.; Schneiderman, R. & Teichner, P.
  
• On the equivalence of Bayesian and dominant strategy implementation. Econometrica, 81(1):197–220, 2013
  A. Gershkov, J. K. Goeree, A. Kushnir, B. Moldovanu, and X. Shi
  
• Optimal asymptotic bounds for spherical designs. Ann. of Math. (2), 178(2):443–452, 2013
  Bondarenko, Andriy; Radchenko, Danylo & Viazovska, Maryna
  
• Plasticity of tumour and immune cells: a source of heterogeneity and a cause for therapy resistance? Nature Rev. Cancer 13(5): 365–376, 2013
  Hölzel, Michael; Bovier, Anton & Tüting, Thomas
  
• Finite time blow-up and condensation for the bosonic Nordheim equation. Invent. Math. 200(3):761–847, 2015
  Escobedo, M. & Velázquez, J. J. L.
  
• Free energy fluctuations for directed polymers in random media in 1+1 dimension. Comm. Pure Appl. Math. 67(7):1129–1214, 2014
  Borodin, Alexei; Corwin, Ivan & Ferrari, Patrik
  
• Investment dispersion and the business cycle. American Economic Review, 104(4):1392–1416, 2014
  Bachmann, Rüdiger & Bayer, Christian
  
• Lines of minima in outer space. Duke Math. J., 163(4):733–776, 2014
  Hamenstädt, Ursula
  
• Lp theory for outer measures and two themes of Lennart Carleson united. Bull. Amer. Math. Soc. (N.S.), 52(2):249–296, 2015
  Do, Yen & Thiele, Christoph
  
• Mean-field evolution of fermionic systems. Comm. Math. Phys. 331(3):1087–1131, 2014
  Benedikter, Niels; Porta, Marcello & Schlein, Benjamin
  
• On the equivalence of the entropic curvaturedimension condition and Bochner’s inequality on metric measure spaces. Invent. Math., 201(3):993–1071, 2015
  Erbar, Matthias; Kuwada, Kazumasa & Sturm, Karl-Theodor
  
• Parity sheaves. J. Amer. Math. Soc. 27(4):1169– 1212, 2014
  Juteau, Daniel; Mautner, Carl & Williamson, Geordie
  
• Rate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control. Arch. Ration. Mech. Anal. 214(3):803–866, 2014
  Herrmann, Michael; Niethammer, Barbara & Velázquez, Juan J. L.
  
• Shorter tours by nicer ears: 7/5-approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs. Combinatorica, 34(5):597–629, 2014
  Sebő, András & Vygen, Jens
  
• The Farrell-Jones conjecture for cocompact lattices in virtually connected Lie groups. J. Amer. Math. Soc., 27(2):339–388, 2014
  Bartels, A.; Farrell, F. T. & Lück, W.
  
• The Hodge theory of Soergel bimodules. Ann. of Math. (2) 180(3):1089–1136, 2014
  Elias, Ben & Williamson, Geordie
  
• Improved smoothed analysis of multiobjective optimization. J. ACM, 62(1):4:1–4:58, 2015
  Brunsch, Tobias & Röglin, Heiko
  
• On torsion in the cohomology of locally symmetric varieties. Ann. of Math. (2), 182(3):945–1066, 2015
  Scholze, Peter
  
• Optimal sales contracts with withdrawal rights. The Review of Economic Studies, 82(2):762–790, 2015
  Krahmer, D. & Strausz, R.
  
• Strategic experimentation with private payoffs. Journal of Economic Theory, 159:531–551, 2015
  Heidhues, Paul; Rady, Sven & Strack, Philipp
  
• Time discrete geodesic paths in the space of images. IAM Journal on Imaging Sciences, 8(3):1457–1488, 2015
  Berkels, B.; Effland, A. & Rumpf, M.
  
• Transience of edge-reinforced random walk. Comm. Math. Phys. 339(1):121–148, 2015
  Disertori, Margherita; Sabot, Christophe & Tarrès, Pierre
  
• A stochastic model for immunotherapy of cancer. Scientific Reports 6 (24169), 2016
  Baar, Martina; Coquille, Loren; Mayer, Hannah; Hölzel, Michael; Rogava, Meri; Tüting, Thomas & Bovier, Anton
  
• Belief propagation, robust reconstruction and optimal recovery of block models. Ann. Appl. Probab. 26(4):2211–2256, 2016
  Mossel, Elchanan; Neeman, Joe & Sly, Allan
  
• Better s-t-tours by Gao trees. Mathematical Programming B 172:191–207, 2018
  Gottschalk, Corinna & Vygen, Jens
  
• Dijkstra meets Steiner: a fast exact goal-oriented Steiner tree algorithm. Mathematical Programming Computation 9:135–202, 2017
  Hougardy, Stefan; Silvanus, Jannik & Vygen, Jens
  
• Dislocation microstructures and strain-gradient plasticity with one active slip plane. J. Mech. Phys. Solids, 93:240–251, 2016
  Conti, Sergio; Garroni, Adriana & Müller, Stefan
  
• Eliminating the pollution effect in Helmholtz problems by local subscale correction. Math. Comp. 86(305):1005–1036, 2017
  Peterseim, Daniel
  
• Functional linear regression with points of impact. Ann. Statist., 44(1):1–30, 2016
  Kneip, Alois; Poß, Dominik & Sarda, Pascal
  
• KPZ reloaded. Comm. Math. Phys. 349(1):165–269, 2017
  Gubinelli, Massimiliano & Perkowski, Nicolas
  
• On the interconnection between the higher-order singular values of real tensors. Numer. Math. 135(3):875–894, 2017
  Hackbusch, Wolfgang & Uschmajew, André
  
• Optimal transport and Skorokhod embedding. Invent. Math. 208(2):327–400, 2017
  Beiglböck, Mathias; Cox, Alexander M. G. & Huesmann, Martin
  
• Projectivity of the Witt vector affine Grassmannian. Invent. Math. 209(2):329–423, 2017
  Bhatt, Bhargav & Scholze, Peter
  
• Quivers with relations for symmetrizable Cartan matrices I: Foundations. (English summary) Invent. Math. 209(1):61–158, 2017
  Geiss, Christof; Leclerc, Bernard & Schröer, Jan
  
• Schubert calculus and torsion explosion. With a joint appendix with Alex Kontorovich and Peter J. McNamara. J. Amer. Math. Soc. 30(4):1023–1046, 2017
  Williamson, Geordie
  
• The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth. Math. Comp. 86(306):1855–1876, 2017
  Griebel, Michael; Kuo, Frances Y. & Sloan, Ian H.
  
• A priori L2 -discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints. Numer. Math. 138(2):273–299, 2018
  Neitzel, I. & Wollner, W.
  
• An optimal control problem governed by a regularized phase-field fracture propagation model. SIAM J. Control Optim. 55(4):2271–2288, 2017
  Neitzel, I.; Wick, T. & Wollner, W.
  
• Bayesian posteriors for arbitrarily rare events. Proceedings of the National Academy of Sciences, 114(19):4925–4929, 2017
  Fudenberg, Drew; He, Kevin & Imhof, Lorens A.
  
• Content-based agendas and qualified majorities in sequential voting. Am. Econ. Rev., 107(6):1477–1506, 2017
  Kleiner, Andreas & Moldovanu, Benny
  
• Energy solutions of KPZ are unique. J. Amer. Math. Soc. 31(2):427–471, 2018
  Gubinelli, Massimiliano & Perkowski, Nicolas
  
• Equivariant properties of symmetric products. J. Amer. Math. Soc., 30(3):673– 711, 2017
  Schwede, Stefan
  
• Learning and price discovery in a search market. The Review of Economic Studies, 85(2):1159–1192, 2017
  Lauermann, Stephan; Merzyn, Wolfram & Virág, Gábor
  
• On the generic part of the cohomology of compact unitary Shimura varieties. Ann. of Math. (2) 186(3):649–766, 2017
  Caraiani, Ana & Scholze, Peter
  
• Stable splittings of Hilbert spaces of functions of infinitely many variables. J. Complexity, 41:126–151, 2017
  Griebel, Michael & Oswald, Peter
  
• The K3 category of a cubic fourfold. Compos. Math., 153(3):586–620, 2017
  Huybrechts, Daniel
  
• An adaptive multiscale approach for electronic structure methods. Multiscale Modeling & Simulation. A SIAM Interdisciplinary Journal, 16(2):752–776, 2018
  Chinnamsetty, Sambasiva Rao; Griebel, Michael & Hamaekers, Jan
  
• Data-driven problems in elasticity. Arch. Ration. Mech. Anal. 229(1):79–123, 2018
  Conti, S.; Müller, S. & Ortiz, M.
  
• Global homotopy theory. New Mathematical Monographs 34. Cambridge University Press, Cambridge, 2018. xviii+828 pp.
  Schwede, Stefan
  
• Global routing with timing constraints. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 37 (2018), 406–419
  Held, Stephan; Muller, Dirk; Rotter, Daniel; Scheifele, Rudolf; Traub, Vera & Vygen, Jens
  
• Image extrapolation for the time discrete metamorphosis model: existence and applications. SIAM J. Imaging Sci. 11(1):834–862, 2018
  Effland, Alexander; Rumpf, Martin & Schäfer, Florian
  
• Multilevel preconditioners for embedded enriched partition of unity approximations. Advanced Modeling and Simulation in Engineering Sciences, 5(1):13, 2018
  Schweitzer, Marc Alexander & Ziegenhagel, Albert
  
• Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality. Adv. Math., 331:58–142, 2018
  Ehrig, Michael & Stroppel, Catharina
  
• Nonparametric analysis of random utility models. Econometrica 86(6):1883-1909, 2018
  Kitamura, Yuichi & Stoye, Jörg
  
• Quasimodularity and large genus limits of Siegel-Veech constants. J. Amer. Math. Soc. 31(4):1059–1163, 2018
  Chen, Dawei; Möller, Martin & Zagier, Don
  
• Relationship of gender differences in preferences to economic development and gender equality. Science 362(6412), 2018. eaas9899
  Falk, Armin & Hermle, Johannes
  
• Renormalization of the two-dimensional stochastic nonlinear wave equations. Trans. Amer. Math. Soc. 370(10):7335–7359, 2018
  Gubinelli, Massimiliano; Koch, Herbert & Oh, Tadahiro
  
• Triangulated surfaces in triangulated categories. J. Eur. Math. Soc., 20(6):1473–1524, 2018
  Dyckerhoff, Tobias & Kapranov, Mikhail