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