## Xin Zhou## Assistant ProfessorAddress: Department of MathematicsSouth Hall, Room 6501 University of California Santa Barbara Santa Barbara, California 93106 USA E-mail: zhou "at" math.ucsb.edu |

We are organizing the **UCSB Differential Geometry Seminar**.

I am a member of the Geometry group. Before moving to UCSB, I was a CLE Moore instructor in the Math department at MIT. I received my PhD from Stanford University in 2013 with Richard M. Schoen as my advisor. Here is my **Curriculum Vitae**.

- Differential Geometry, Calculus of Variations, General Relativity.

- NSF Career Award, DMS-1945178, 2020-2024.
- Alfred P. Sloan Research Fellow, 2019-2021.
- NSF Grant DMS-1811293, 2018-2021.
- UC Regent's Junior Faculty Award, 2018.
- NSF Grant DMS-1704393, DMS-1406337, 2014-2017.

- Generic scarring for minimal hypersurfaces along stable hypersurfaces (with A. Song),
*arXiv:2006.03038.* - Min-max theory for free boundary minimal hypersurfaces II -- General Morse index bounds and applications (with Q. Guang, M. Li, and Z. Wang),
*arXiv:1907.12064.* - On the Multiplicity One Conjecture in min-max theory,
*arXiv:1901.01173.* - Compactness and generic finiteness for free boundary minimal hypersurfaces (I) (with Q. Guang and Z. Wang),
*arXiv:1803.01509*. - Free boundary minimal hypersurfaces with least area (with Q. Guang and Z. Wang),
*arXiv:1801.07036*.

- Min-max theory for networks of constant geodesic curvature (with J. Zhu),
*Adv. Math. 361 (2020), 106941, 16 pp*. - Existence of hypersurfaces with prescribed mean curvature I - Generic min-max (with J. Zhu),
*Cambridge Journal of Mathematics, Volume 8, Number 2, 311-362, 2020*. - Min-max minimal disks with free boundary in Riemannian manifolds (with L. Lin and A. Sun),
*Geometry & Topology 24 (2020) 471-532*. - Min-max theory for constant mean curvature hypersurfaces (with J. Zhu),
*Invent. Math. (2019) 218:441-490*. - Min-max theory for free boundary minimal hypersurfaces I - Regularity theory (with M. Li), accepted by
*J. Differential Geometry*,*arXiv:1611.02612.* - A maximum principle for free boundary minimal varieties of arbitrary codimension (with M. Li), accepted by
*Comm. Anal. Geom.*,*arXiv:1708.05001.* - Curvature estimates for stable free boundary minimal hypersurfaces (with Q. Guang and M. Li),
*J. reine angew. Math. 759 (2020), 245-264*. - Sweeping out 3-manifold of positive Ricci curvature by short 1-cycles via estimates of min-max surfaces (with Y. Liokumovich),
*Int. Math. Res. Not. IMRN 2018, no. 4, 1129-1152*. - Entropy of closed surfaces and min-max theory (with D. Ketover),
*J. Differential Geom. 110 (2018), no. 1, 31-71.* - Existence of minimal surfaces of arbitrarily large Morse index (with H. Li),
*Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 64, 12 pp.* - Min-max hypersurface in manifold of positive Ricci curvature,
*J. Differential Geom. 105 (2017), no. 2, 291-343.* - On the free boundary min-max geodesics,
*Int. Math. Res. Not. IMRN 2016, no. 5, 1447-1466*. - Min-max minimal hypersurface in \( (M^{n+1}, g) \) with \( Ric_g>0 \) and \( 2\leq n\leq 6 \),
*J. Differential Geom. 100 (2015), no. 1, 129-160.* - Mass angular momentum inequality for axisymmetric vacuum data with small trace,
*Comm. Anal. Geom. 22 (2014), no. 3, 519-571.* - Convexity of reduced energy and mass angular momentum inequalities (with R. Schoen),
*Ann. Henri Poincare 14 (2013), no. 7, 1747-1773.* - On the existence of min-max minimal surfaces of genus g≥ 2,
*Commun. Contemp. Math. 19 (2017), no. 4, 1750041, 36 pp.* - On the existence of min-max minimal torus,
*J. Geom. Anal. 20 (2010), no. 4, 1026-1055.*

- Multiplicity One Conjecture in min-max theory,
*Partial Differential Equations, Oberwolfach Report 2019*. - On the Multiplicity One Conjecture in min-max theory,
*Surveys in Geometric Analysis 2019*, to appear. - Min-max theory for constant mean curvature (CMC) hypersurfaces (with Jonathan Zhu),
*Partial Differential Equations, Oberwolfach Report No. 35/2017*. - On minimal surfaces with free boundary (with Martin Li),
*special issues of ICCM Notices*, to appear. - Recent progress on compactness of minimal surfaces with free boundary (with Qiang Guang),
*Surveys in Geometric Analysis 2017, 63-78, Science Press Beijing, Beijing, 2018. ISBN: 9787030573223*.

*Lectures on minimal surfaces*: This series of lecture notes were taken by Junrong Yan for the topic course I taught during Fall 2017.*Introduction to the min-max theory for minimal surfaces*: Hand-written lecture notes for a topic course on the min-max theory of minimal surfaces in 2013.*Lecture notes on minimal surfaces*: This series of lecture notes were taken for the topic course on minimal surfaces given by Professor Rick Schoen in the Winter quarter of 2012 at Stanford.*Introduction to Mathematical General Relativity*: This series of lecture notes were taken for the topic course on mathematical General Relativity given by Professor Rick Schoen in the spring quarter of 2012 at Tsinghua University.

*Multiplicity One Conjecture in min-max theory (Part I)**(Part II)*: This is the video of the lectures given in the Variational Methods in Geometry Seminar, IAS, March 2019.*Min-max theory for constant mean curvature (CMC) hypersurfaces*: This is the video of the lecture given in the Workshop: Mass in General Relativity at Simons Center, Stony Brook, March 2018.*Min-max minimal hypersurface with free boundary*: This is the video of the lecture given in the Geometric Analysis and General Relativity workshop at BIRS, Banff, July 2016.

- Fall 2016.
*Math 240A: Lectures on Differential Geometry.* - Winter 2017.
*Math 240B: Riemannian Geometry*and*Math 117: Methods of Analysis*. - Fall 2017.
*Math 241A: Topics in Differential Geometry*,*Math 117: Methods of Analysis*. - Spring 2018.
*Math 8: Transition to higher mathematics*. - Fall 2019.
*Math 4B: Differential Equations*. - Winter 2020.
*Math 6A: Vector Calculus I*and*Math 240B: Riemannian Geometry*.