EXC 59:  Mathematics: Foundations, Models, Applications

• Subject Area: Mathematics ; Computer Science ; Economics
• Term: from 2006 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 24102279

• Final Report Year: 2019

Final Report Abstract

The Hausdorff Center for Mathematics (HCM) has used the unique opportunities provided by the Excellence Initiative to establish a sustainable world-class center for cutting-edge mathematical research in Germany, on a par with the mathematics departments of top universities in Europe and in the US. HCM fosters fundamental research in mathematics and responds to the demands of science and society with mathematical insights and tools. Particular foci of research conducted by HCM included: - arithmetic algebraic geometry, - representation theory and topology, - geometry, metric-measure spaces, and optimal transport, - singular stochastic partial differential equations and harmonic analysis, - mathematical models of materials and virtual material design, - mathematical models in immunology, - mechanism design and game theory, - imaging and geometry processing, algorithms, complexity, and combinatorial optimization. HCM strengthened its team of internationally outstanding scientists by strategic hirings from Berkeley, Oxford, Paris, and Los Angeles, and retained its faculty against highly competitive offers from Chicago, Harvard, MIT, Northwestern, Oxford, Princeton, and Yale. Researchers at HCM were recognized with high honors (e.g., Fields Medal, 4 Leibniz Prizes, 5 ERC Advanced Grants). The Hausdorff Research Institute for Mathematics, founded in 2006 as part of the HCM, has become a leading institute for thematic programs in mathematics. HCM established internationally visible recruiting and training programs - with particular emphasis on early independence, gender balance, and internationalization - that provide entry points for outstanding young researchers from all over the world into the German university system. The Bonn International Graduate School of Mathematics was established as a common entry point for doctoral students; the GlobalMathNetwork facilitates the international exchange of doctoral researchers within a network with some of the best research centers and graduate schools in mathematics across the globe. The Hausdorff School for Advanced Studies in Mathematics has set up an innovative training program - unparalleled so far - for postdoctoral researchers based in Germany and worldwide. The Bonn Junior Fellows program offers temporary W2 professor positions to excellent early-career Researchers.

Link to the final report

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

Publications

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