Curriculum Vitae

Ke Zhu                                                                                                        Curriculum Vitae

Address  Department of Mathematics and Statistics             Email: ke.zhu@mnsu.edu

Minnesota State University Mankato                       Phone: 507-389-1039 (O)

250 Wissink Hall

Mankato, MN 56001

Education

Stanford University, Ph.D. in Mathematics                                                      1999-2004

Peking University, P.R. China, M.S. in Mathematics                                       1996-1999

Nankai University, P.R. China, B.S. in Mathematics                                        1992-1996

Employment

Minnesota State University Mankato, Associate Professor                              2019-present

Minnesota State University Mankato, Assistant Professor                              2016-2019

Minnesota State University Mankato, Instructor                                              2014-2016

Harvard University, Postdoctoral Fellow                                                          2012-2014

University of Minnesota, Visiting Assistant Professor                                      2010-2012

The Chinese University of Hong Kong, Research Associate                           2008 -2010

University of Wisconsin-Madison, Van Vleck Visiting Assistant Professor      2005-2008

The Fields Institute and University of Toronto, Postdoctoral Fellow                2004-2005

Research Interest

    Geometric Analysis:  Cauchy-Riemann and Dirac type equations with geometric applications, isometric embedding of Riemannian manifolds by eigenfunctions and heat kernel, instantons in G2 manifolds and relations to Seiberg-Witten invariants

    Symplectic Topology: Floer homology and applications to Hamiltonian dynamic systems, Legendrian contact homology and application to knot invariants, quantum invariants from J-holomorphic curves and gauge theory, moduli space techniques (including transversality, compactification, gluing, and degeneration) for topological invariants

Research Works

Papers:

  • Thick-Thin decomposition of Floer trajectories and adiabatic gluing, (arXiv: 1103.3525), 94pp, to appear in Acta Mathematica Sinica, English Series, 2023, with Yong-Geun Oh
  • High-jet relations of the heat kernel embedding map and applications, (arXiv: 1308.0410), to appear in 2021-2022 MATRIX Mathematical Research Institute Annals
  • Solvability of Dirac Type Equations (arXiv: 1407.6936), Adv. Math., (320C), 2017, 451-474, with Qingchun Ji
  • Isometric embeddings via heat kernel (arXiv: 1305.5613), J. Diff. Geom., (99), 2015, 497-538, with Xiaowei Wang
  • Thin instantons in G2-manifolds and Seiberg-Witten invariants, (arXiv: 1107.1947), J. Diff. Geom., (95), 2013, 419-481, with Conan Leung and Xiaowei Wang
  • Floer trajectories with immersed nodes and scale-dependent gluing (arXiv:0711.4187), J. Symplectic Geometry, Vol.9, No.4, 483-636, 154pp, 2011, with Yong-Geun Oh
  • Instantons in G2-manifolds from J-holomorphic curves in coassociative submanifolds (arXiv:1303.6728), Proceedings of Gokova Geometry-Topology 2012, 89-110, with Conan Leung and  Xiaowei Wang
  • Embedding property of J-holomorphic curves in Calabi-Yau manifolds for generic J (arXiv:0805.3581), Asian Journal of Math, Vol.13, No.3, 323-340, 2009, with Yong-Geun Oh

Preprints:

  • Moduli spaces of J-holomorphic curves with general jet constraints, arXiv: 0911.1710
  • Conformal embeddings via heat kernel, with Xiaowei Wang, preprint 2014
  • Moment map, heat kernel and balanced embedding, preprint, with Xiaowei Wang
  • Dirac operators on thin manifolds and boundary elliptic regularity, preprint, with Conan Leung and Xiaowei Wang

 Work in Progress:

  • Transversality of holomorphic curves via curvature integrals, with Qingchun Ji
  • Thin instantons in G2-manifolds bounding intersecting coassociative submanifolds, with Conan Leung and Xiaowei Wang

Thesis:

  • Degeneration of J-holomorphic disc moduli spaces and Legendrian contact homology, Ph.D. Thesis (2004) Stanford University
  • Helfrich energy on closed surfaces and membrane shapes of blood cells, M.S. Thesis (1999), Peking University, Beijing, China

 Expository Notes:

  • Knot surgery for Lagrangian surfaces in 4-dimensional symplectic space (research notes, 2002)
  • Introduction to geometric phase in dynamic systems (writing project, 2001)                         

Teaching Experience

Minnesota State University Mankato

  • Math 611 Measure Theory                                                                 2018, 2022 Spring
  • Math 692 Topology                                                                             2017, 2021 Spring
  • Math 680 Nonlinear Dynamics                                                                         2016 Fall
  • Math 499 Differential Topology (individual study)                                        2017 Spring
  • Math 492W Mathematics Capstone Experience                                2017~2021 Fall
  • Math 447/547 Linear Algebra II                                              2016, 2019~2021 Spring
  • Math 321 Ordinary Differential Equations                                     2015, 2017, 2018 Fall
  • Math 247 Linear Algebra I                               2017, 2018, 2022 Spring, 2023 Summer
  • Math 223 Calculus III                                                                           2022 Spring
  • Math 122 Calculus II                           2014 Fall, 2015~2016 Spring, 2019~2021 Fall
  • Math 121 Calculus I                                            2015 Fall, 2019 Spring, 2021 Summer
  • Math 115 Precalculus                                                2014 Fall, 2015 Spring, 2016 Fall
  • Participated iSALT program (Institute for the Scholarship of Assessment, Learning and Teaching) in The Center for Excellence in Teaching & Learning                       2015 Fall
  • Completed Faculty Teaching Certificate Program in The Center for Excellence in Teaching & Learning                                                                                            2014 Fall

University of Minnesota

  • Math 1271 Calculus (I)                                                               2011 Spring, 2010 Fall

The Chinese University of Hong Kong

  • Abstract Algebra I                                                                                             2009 Fall
  • Undergraduate Seminar of Projective Geometry                                  2009 Spring, Fall
  • Graduate Symplectic Topology (basic sympletic geometry, J-holomorphic curves, Morse homology and Floer homology)                                                                                                         2008 Fall

University of Wisconsin-Madison

  • Math 751: Algebraic Topology I (graduate course)                                          2006 Fall
  • Math 551: Elementary Topology                                                                  2006 Spring
  • Math 340: Linear Algebra                                                                             2008 Spring
  • Math 320: Ordinary Differential Equations and Linear Algebra                    2006 Spring
  • Math 319: Techniques in Ordinary Differential Equations           2005 Fall, 2006 Spring
  • Math 234: Multivariable Calculus                                                              2006 Summer
  • Math 217: Calculus with Algebra and Trigonometry II                                 2006 Spring
  • Math 213: Calculus and Introduction to Differential Equations    2005, 2006, 2007 Fall
  • Math 112: College Algebra                                                                              2007 Fall

University of Toronto

  • Math 135Y: Single Variable Calculus                                           2004 Fall and Winter

Stanford University

Teaching Assistant:

  • Math 51h : Honors Linear Algebra and Multivariable Calculus            2001,2003 Fall
  • Math 205C: Real Analysis Qualifying Exam Seminar (for entry graduates) 2003 Spring
  • Math 52:    Multivariable Calculus and Analytical Geometry                    2002 Winter

Course Assistant:

  • Math 120: Abstract Algebra I                                                                   2001 Spring
  • Math 173: Differentiable Manifolds                                                              2000 Fall

Computer Skills

MS Office, LaTeX, MATLAB, SAGE, Python, Machine Learning (Coursera certificate in 2018), basic web editing

Awards and Honors

In U.S.

  • Minnesota State University Faculty Improvement Grant ($1800)  2022
  • Minnesota State University Presidential Teaching Scholar Fellowship ($7300)               2018
  • NSF support for Ph.D. thesis research in Stanford University  ($3000)       July-August, 2004
  • Teaching and Research Scholarships in Stanford University                                   1999-2003

In China

  • Jiu Zhang Math Prize (National prize for top math undergraduates)                     1994
  • First Prize Winner of National High School Mathematics League in China          1991

Invited Talks

Partial Collapsing Degeneration of Floer Trajectories and Adiabatic Gluing

AMS Sectional Meeting “Quantitative Aspect of Symplectic Topology”    April, 2023

High-jet Relations of the Heat Kernel Embedding Map and Applications

Symplectic Topology Seminar in University of Minnesota                      March, 2023

Thick-thin Decomposition of Floer Trajectories and Adiabatic Gluing

   Symplectic Topology Seminar in University of Minnesota                      November, 2021

Ricci Flow and Recent Applications

Colloquium in Minnesota State University Mankato                                       April 2021

Experience in 2019 Workshop at Center for Project-Based Learning in WPI

Colloquium in Minnesota State University Mankato                                September 2019

Redesigning the Math Capstone Course: A Comprehensive Approach

Scholars at Work Conference, Minnesota State University Mankato            March, 2019

Solvability of Dirac Type Equations and Transversality of Holomorphic Curves

Mini-Workshop on Symmetries of Symplectic 4-manifolds and Peudo-holomorphic Curves in University of Minnesota,                                                                                 May 2018

Solvability of Dirac Type Equations

MAA North Central Sectional Meeting                                                               April 2018

Isometric embedding via heat kernel

Geometry and Topology Seminar in University of Wisconsin-Madison   September  2017

Isometric embeddings via heat kernel

Differential Geometry seminar in University of California Irvine                    June 2017

Solvability of the Dirac Equation

AMS Sectional Meeting “Symplectic and Contact Geometry”                   October 2016

Dynamics, Floer homology and knot invariants

Colloquium in Minnesota State University Mankato                                       April 2016

The Poincare-Birkhoff theorem and the billiard problem

Colloquium in Minnesota State University Mankato                                 October, 2015

Isometric embeddings via heat kernel

North Central Section MAA Meeting, Winona State University                      April, 2015

Solvability of the Dirac Equation

Professor Yau’s student seminar in Harvard University                              March 2015

Isometric embeddings of Riemannian manifolds via heat kernel                    

Colloquium in Georgia Southern University                                           February, 2015

Isometric embeddings via heat kernel                    

Colloquium in Minnesota State University Mankato                                October, 2014

Solvability of the Dirac Equation

Differential Geometry and Symplectic Topology Seminar in University of Minnesota

August, 2014

A glimpse into Riemann surfaces

“Year of Germany” talk in Dept. of Math. Univ. Wisconsin-River Falls   November, 2013

Isometric embeddings via heat kernel

Gauge Theory and Topology Seminar in Harvard University                   October, 2013

Isometric embeddings via heat kernel

Geometry Seminar in Boston University                                                   October, 2013

Isometric embeddings via heat kernel

Differential Geometry and Symplectic Topology Seminar in University of Minnesota

September, 2013

Thin instantons in G2-manifolds and Seiberg-Witten invariants

Special Seminar in Center for Geometry and Physics of Institute for Basic Science, Pohang, Korea                                                                                                 January, 2013

Thick-thin decomposition of Floer trajectories and adiabatic gluing

Geometry Seminar in University of Rochester                                      December, 2012

Thin instantons in G2-manifolds and Seiberg-Witten invariants

   Integrable Systems Seminar in University of Arizona                          November, 2012

Thin instantons in G2-manifolds and Seiberg-Witten invariants

   Gauge Theory and Topology Seminar in Harvard University              September, 2012

Thick-thin decomposition of Floer trajectories and adiabatic gluing

Geometry Seminar in Peking University                                                        May, 2012

Thin instantons in G2-manifolds and Seiberg-Witten invariants

   Geometry Seminar in University of Rochester                                      November, 2011

Thin instantons in G2-manifolds and Seiberg-Witten invariants

   Geometry Seminar in Michigan State University                                  September, 2011

Thin instantons in G2-manifolds and Seiberg-Witten invariants

Geometry and Topology Seminar in University of Wisconsin-Madison, September, 2011

Thin instantons in G2-manifolds and Seiberg-Witten invariants

   Symplectic Topology Seminar in University of Minnesota                             April, 2011

Thick-thin decomposition of Floer trajectories and adiabatic gluing

Geometry Seminar in Stanford University                                                     March, 2011

Thick-thin decomposition of Floer trajectories and adiabatic gluing

Geometry and Topology Seminar in University of Wisconsin-Madison,   October, 2010

Thick-thin decomposition of Floer trajectories and adiabatic gluing

Symplectic Topology Seminar in University of Minnesota                  September, 2010

Jet Evaluation Transversality of J-holomorphic Curves and Applications

Symplectic Topology Seminar in University of Minnesota,                  November, 2009

Embedding property of J-holomorphic curves in Calabi-Yau manifolds for generic J

   Geometry Seminar in Hong Kong University, Hong Kong                    September, 2009

Embedding property of J-holomorphic curves in Calabi-Yau manifolds for generic J

Symplectic Geometry Seminar in Stanford University, Stanford             August, 2009

Floer Trajectories with Immersed Nodes and Scale-dependent Gluing

National Cheng Kung University, Tainan, Taiwan                                         May, 2009

Embedding property of J-holomorphic curves in Calabi-Yau manifolds for generic J

National Cheng Kung University, Tainan, Taiwan                                        May, 2009

Embedding property of J-holomorphic curves in Calabi-Yau manifolds for generic J

Hong Kong Geometry Colloquium, Hong Kong                                       October, 2008

Embedding property of J-holomorphic curves in Calabi-Yau manifolds for generic J

Seminar in Korea Institute for Advanced Study, Seoul                                  June, 2008

Floer Trajectories with Immersed Nodes and Scale-dependent Gluing

Symplectic Topology Seminar in University of Montreal, Canada         February, 2008

Floer Trajectories with Immersed Nodes and Scale-dependent Gluing

Geometry and Topology Seminar in University of Wisconsin-Madison October, 2007

Scale-dependent Gluing, Floer Trajectories with Immersed Nodes and the PSS map

Differential Geometry and Symplectic Topology Seminar in University of Minnesota                                                             August, 2007

Degeneration of J-holomorphic Disc Moduli Space and Legendrian Contact Homology

Korea Institute for Advanced Study, Seoul                                                  July, 2005

Degeneration of J-holomorphic Disc Moduli Space and Legendrian Contact Homology      

Geometry/Topology Seminar in Peking University, Beijing                         May, 2005

Degeneration of J-holomorphic Disc Moduli Space and Legendrian Contact Homology      

Geometry/Topology Seminar in McMaster University                              January, 2005

Gromov-Witten Theory, Contact Geometry and Moduli Space Degeneration

Geometry Seminar in Chinese Academy of Sciences, Beijing          December, 2004

Degeneration of J-holomorphic Disc Moduli Space and Legendrian Contact Homology

     String Theory Seminar in The Fields Institute                                       October, 2004

The Degeneration of J-Holomorphic Discs to Gradient Flow Trees and Braid Invariants

University of South California/Caltech Joint Geometry Seminar           October, 2003

Gradient Flow Trees and Legendrian Contact Homology

Stanford Symplectic Geometry Seminars                                              October, 2003

The Degeneration of J-Holomorphic Discs to Gradient Flow Trees

AIM Conference “ Holomorphic Curves in Contact Geometry”         August, 2003

Moduli Spaces of Metric Ribbon Trees and Genus Zero Marked Riemann Surfaces

Stanford Symplectic Geometry Seminar                                                   January, 2003

Professional Service

  • Referee for Kyoto Journal of Mathematics 2023
  • Referee for Geometry & Topology 2023
  • Referee for Journal of Symplectic Geometry                                                                 2012
  • Referee for Advances in Mathematics                                                                             2008
  • Co-organizer of 2018 MAA North Central Sectional Meeting at Minnesota State University Mankato, April  2018
  • Co-organizer of AMS Sectional Meeting “Symplectic and Contact Geometry”  at University of St. Thomas,   October 2016
  • Co-organizer of Geometry and Topology Seminars in University of Wisconsin-Madison           09/2005-05/2007
  • Member of Faculty Advancement Committee in Department of Mathematics & Statistics at Minnesota State University Mankato                                                                              2014-2018
  • Member of Advisory Committee of Master Thesis defense of 6 students in Department of Mathematics & Statistics at Minnesota State University Mankato                              2016-2017
  • Member of High School Mathematics Contest Committee in Minnesota State University Mankato              2018-present
  • Member of Curriculum Committee in Department of Mathematics & Statistics at Minnesota State University  2019-present

Student Advising

  • Alexander Harr, Master Thesis Heat Kernel Voting with Geometric Invariants, 2020
  • Katelyn Laporte, Master APP Conformal Deformation of Surfaces by the Extrinsic Dirac Operator, 2021 

Conferences Attended

AMS Sectional Meeting “Quantitative Aspect of Symplectic Topology”, University of Cincinnati, April, 2023

IBS-CGP & MATRIX workshop on Symplectic Topology, MATRIX Institute in University of Melbourne, December 2022

Yamabe Memorial Symposium                            University of Minnesota, October, 2022

Floer Homotopy Theory (Hybrid Workshop)         MSRI, UC Berkeley, September, 2022

Algebraic Topology: Methods, Computation and Science (conference was cancelled due to pandemic, but some talks were moved online), Ohio State University, June, 2020

Current Developments in Mathematics,     Harvard University, November, 2019

Institute for Project Based Learning Workshop   Worcester Polytechnic Institute, June, 2019

26th Southern California Geometric Analysis Seminar                 UCSD, January, 2019

Yamabe Memorial Symposium: Moduli Spaces in Algebraic Geometry             University of Minnesota, September, 2018

Geometry Methods in Symplectic and Contact Topology (conference in honor of Yakov Eliashberg)                                       Stanford University, August, 2018

Mini-Workshop on Symmetries of Symplectic 4-manifolds and Peudo-holomorphic Curves                           University of Minnesota, May, 2018

Topological Data Analysis: Theory and Applications        Macalaster College, June, 2017

Journal of Differential Geometry Conference 2017           Harvard University, May, 2017

24th Southern California Geometric Analysis Seminar                 UCSD, February, 2017

NSF-CBMS Regional Conference Topological Data Analysis, U Texas-Austin, June,2016

Current Developments in Mathematics 2015             Harvard University, November, 2015

Fifth Abel Conference: Mathematical Impact of John Nash Jr. and Louis Nirenberg                                        

                                                                     IMA, University of Minnesota, August, 2015

Journal of Differential Geometry Conference 2014 Harvard University, September, 2014

Workshop on Moduli Spaces of Pseudo-holomorphic Curves I,                      March, 2014

Simons Center for Geometry and Physics, Stony Brook

Current Developments in Mathematics 2013           Harvard University, November, 2013

Workshop and Conference on the Topology and Invariants of Smooth 4-Manifolds

                                                                               University of Minnesota, August, 2013

Current Developments in Mathematics 2012             Harvard University, November, 2012

Cycles, Calibrations and Nonlinear PDE             Stony Brook University, October, 2012

Yamabe Memorial Symposium                         University of Minnesota, September, 2012

Holomorphic Curves and Low Dimensional Topology Stanford University, August, 2012

Symplectic Geometry and Mathematical Physics   Peking University, Beijing, May, 2012

Great Lake Geometry Conference                                 Ohio State University, April, 2012

Mirror Symmetry in the Midwest Conference   Kansas State University, November, 2011

Workshop on sheaf-theoretic methods in symplectic topology   IAS, Princeton, May, 2011

Great Lake Geometry Conference                              Ohio State University, March, 2011

Yamabe Memorial Symposium                             University of Minnesota, October, 2010

Mini-Conference in Geometry          The Chinese University of Hong Kong, March, 2010

Algebraic Structures in the Theory of Holomorphic Curves   MSRI, Berkeley, Nov, 2009      

Symplectic Geometry and Physics                          Peking University, Beijing, May, 2009

East Asian Symplectic Conference                          Academia Sinica, Taipei, May, 2009

Yamabe Memorial Symposium                         University of Minnesota, September, 2008

Holomorphic Curves, Algebraic Structures and Applications      Stanford, August, 2008

Floer Theory and Symplectic Dynamics                       University of Montreal, May, 2008

Workshop of Mirror Symmetry                                 University of Michigan, April, 2008

Great Lake Geometry Conference                   University of Minnesota, September, 2007                      

New Perspectives and Challenges in Symplectic Field Theory         Stanford, June, 2007

Yamabe Memorial Symposium                        University of Minnesota, September, 2006

New Developments in the Geometry and Physics of Gromov-Witten Theory

MSRI, Berkeley, May, 2006

Thematic Program on String Theory                   The Fields Institute, Toronto, 2004-2005

Workshop on Mirror Symmetry            The Primeter Institute, Waterloo, November, 2004

Morse Theoretic Methods in Non-linear Analysis and Symplectic Topology                                            

University of Montreal, June, 2004

Symplectic Geometry and Mathematical Physics               MSRI, Berkeley, March, 2004

Amoebas and Tropical Algebraic Geometry                     AIM, Palo Alto, October, 2003

Holomorphic Curves in Contact Geometry                         AIM, Palo Alto, August, 2003

Holomorphic Curves in Symplectic Geometry                       IAS, Princeton, Winter, 2002

Summer School in Symplectic Geometry               University de Jussieu, Paris, July, 2001

 

Memberships

Member of American Mathematics Society                                                    1999-present

Member of Mathematical Association of American                                          2003-2004