Xuanyu Li
Ph.D. Student
Daniel Stern
Assistant Professor
Publications
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Existence of harmonic maps and eigenvalue optimization in higher dimensions (with M. Karpukhin), arXiv preprint, arXiv:2207.13635.
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Quantization and non-quantization of energy for higher-dimensional Ginzburg—Landau vortices (with A. Pigati), Ars Inveniendi Analytica (2023), Paper No. 3, 55p.
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From Steklov to Laplace: free boundary minimal surfaces with many boundary components (with M. Karpukhin), arXiv preprint, arXiv:2109.11029.
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Min-max harmonic maps and a new characterization of conformal eigenvalues (with M. Karpukhin), arXiv preprint, arXiv:2004.04086.
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Harmonic functions and the mass of 3-dimensional asymptotically flat Riemannian manifolds (with H. Bray, D. Kazaras, and M. Khuri), Journal of Geometric Analysis, vol. 32 (2022).
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Scalar curvature and harmonic maps to S^1, Journal of Differential Geometry, vol. 122 no. 2 (2022), 259—269.
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Minimal submanifolds from the abelian Higgs model (with A. Pigati), Inventiones Mathematicae, vol. 223 (2021), 1027—1095.
Education
- Ph.D. (2019) Princeton University
Departments and programs
Links
Yusheng Luo
Assistant Professor
Publications
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(with R. Lodge and S. Mukherjee) On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps, Geom. Funct. Anal., 32:1428–1485, 2022.
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(with R. Lodge and S. Mukherjee) Circle packings, kissing reflection groups and critically fixed anti-rational maps, Forum Math. Sigma, 10: e3, 2022.
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On geometrically finite degenerations I: boundaries of main hyperbolic components, J. Eur. Math. Soc. (JEMS), to appear, 2021.
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Trees, length spectra for rational maps via barycentric extensions and Berkovich spaces, Duke Math. J., 171(14): 2943–3001, 2022.
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Limits of rational maps, R-trees and barycentric extension, Adv. Math., 394:108075, 2021.
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On the inhomogeneity of Mandelbrot set, Int. Math. Res. Not. IMRN, 2021(8):6051–6076, 2021.
Education
- Ph.D. (2019) Harvard University
Departments and programs
Links
Jun Michael Ling
Visiting Professor
Publications
- The square of Nijenhuis tensor and its vanishing results, Asian-European Journal of Mathematics, volume 15 (2022), no 8.
- (joint with X.~Cao, S.~Hou) Estimate andmonotonicity of the first eigenvalue under Ricci Flow, Math. Ann. volume 354 (2012), pages 451–463.
- Estimates on the lower bound of the first gap, Comm. Anal. Geometry, volume 16 (2008), no 3 539-563.
- The first eigenvalue of a closed manifold with positive Ricci curvature, Proc. Amer. Math. Soc., volume 134 (2006), no. 10, 3071-3079.
Juliet Aygun
Ph.D. Student
Emily Witt
Michler Scholar
Publications
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Lower bounds on the F-pure threshold and extremal singularities, with Z. Kadyrsizova, J. Kenkel, J. Page, J. Singh, K. E. Smith, and A. Vraciu, to appear in Transactions of the American Mathematical Society
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Frobenius powers, with D. Hernández and P. Teixeira, Mathematische Zeitschrift 296 (2020), no. 1-2, 541-572
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Connectedness and Lyubeznik numbers, with L. Núñez-Betancourt and S. Spiroff, International Mathematics Research Notices 2019 (2019), no. 13, 4233-4259
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Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians, with C. Raicu and J. Weyman, Advances in Mathematics 250 (2014), 596-610.
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Local cohomology with support in ideals of maximal minors, Advances in Mathematics 231 (2012) 1998-2012
Education
- Ph.D. (2011) University of Michigan
Departments and programs
Links
Gaoming Wang
Visiting Assistant Professor
Publications
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Curvature estimates for stable minimal surfaces with a common free boundary. Calc. Var. 61, 138 (2022). https://doi.org/10.1007/s00526-022-02226-3
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Uniformization of surfaces with boundary and the application to the triple junction surfaces with negative Euler characteristic, submitted, arXiv:2110.12656, 2021.
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Index of Embedded Networks in the Sphere, submitted, arXiv:2110.12653, 2021.
Education
- Ph.D. (2022) The Chinese University of Hong Kong
Departments and programs
Links
Ritvik Ramkumar
H.C. Wang Assistant Professor
Publications
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Rational singularities of nested Hilbert schemes (with Alessio Sammartano) (arxiv.2109.09002)
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The fiber-full scheme (with Yairon Cid-Ruiz) (arxiv.2108.13986)
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On the tangent space to the Hilbert scheme of points in P^3 (with Alessio Sammartano), Transactions of the American Mathematical Society 375: 6179-6203 (2022).
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The Hilbert scheme of a pair of linear spaces, Mathematische Zeitschrift 300: 493-540 (2022)
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On the smoothness of lexicographic points on Hilbert schemes (with Alessio Sammartano), Journal of Pure and Applied Algebra 226: Article 106872 (2022)
Education
- Ph.D. (2022) University of California, Berkeley
Departments and programs
Links
Christian Gaetz
Klarman Fellow
Publications
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Balance constants for Coxeter groups, with Yibo Gao. Preprint (2020).
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Spherical Schubert varieties and pattern avoidance. Selecta Mathematica (2022).
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Stable characters from permutation patterns, with Christopher Ryba. Selecta Mathematica (2021).
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Separable elements and splittings of Weyl groups, with Yibo Gao. Advances in Mathematics (2020).
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A combinatorial sl(2)-action and the Sperner property for the weak order, with Yibo Gao. Proceedings of the American Mathematical Society (2020).
Education
- Ph.D. (2021) Massachusetts Institute of Technology