Tian Yang 
Associate Professor 




My Curriculum Vitae.
Preprints:
Joint with Giulio Belletti, Asymptotics of quantum 6jsymbols and generalized hyperbolic tetrahedra.
Joint with Francis Bonahon and Helen Wong, Asymptotics of quantum invariants of surface diffeomorphisms II: the figureeight knot complement.
Joint with Francis Bonahon and Helen Wong, Asymptotics of quantum invariants of surface diffeomorphisms I: conjecture and algebraic computations.
Joint with Ka Ho Wong, Asymptotic expansion of relative quantum invariants.
Joint with Ka Ho Wong, Relative ReshetikhinTuraev invariants, hyperbolic cone metrics and discrete Fourier transforms II.
Joint with Giulio Belletti, Discrete Fourier transforms, quantum 6jsymbols and deeply truncated tetrahedra.
Joint with Ka Ho Wong, On the Volume Conjecture for hyperbolic Dehnfilled 3manifolds along the figureeight knot.
Selected Publications:
Joint with Ka Ho Wong, Adjoint twisted Reidemeister torsion and Gram matrices, Advances in Mathematics 438 (2024), Paper No. 109470, 45 pp.
A relative version of the TuraevViro invariants and the volume of hyperbolic polyhedral 3manifolds, Journal of Topology 16 (2023), no.2, 650678.
Joint with Ka Ho Wong, Relative ReshetikhinTuraev invariants, hyperbolic cone metrics and discrete Fourier transforms I, Communications in Mathematical Physics 400 (2023) 10191070.
Joint with Giulio Belletti, Renaud Detcherry and Efstratia Kalfagianni, Growth of quantum 6j symbols and applications to the Volume Conjecture, Journal of Differential Geometry 120 (2022) 199229.
Joint with Sara Maloni and Frederic Palesi, On typepreserving representations of threepuncture projective plane group, Journal of Differential Geometry 119 (2021) 421457.
Joint with Renaud Detcherry and Efstratia Kalfagianni, TuraevViro Invariants, Colored Jones Polynomials and Volume, Quantum Topology 9 (2018), no. 4, 775813.
Joint with Qingtao Chen, Volume Conjectures for the ReshetikhinTuraev and the TuraevViro Invariants, Quantum Topology 9 (2018), no. 3, 419–460.
On TypePreserving Representations of the FourPunctured Sphere Group, Geometry & Topology 20 (2016), 1213–1255.
Joint with Feng Luo, Volume and Rigidity of Hyperbolic Polyhedral 3Manifolds, Journal of Topology 11 (2018), no.1, 129.
Joint with Julien Roger, The Skein Algebra of Arcs and Links and the Decorated Teichmuller Space, Journal of Differential Geometry 96 (2014), no.1, 95140.
A Deformation of Penner's Simplicial Coordinate, Journal of Differential Geometry 89 (2011), no.3, 529551.
Lecture notes:
Spring 2016, Math28401: An Introduction to Quantum Topology. Lecture notes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
Talks:
2024
April 2628, plenary speaker, Knots in Washington 49.984375, George Washington University, Washington DC.
April 19, seminar talk, Topology Seminar, Texas State University, San Marcos, TX.
January 36, invited speaker, AMS 2024 Joint Mathematics Meetings, Special Session on Knots, Skein Modules, and Categorification, Moscone North/South, Moscone Center, San Francisco, CA.
2023
October 30, Seminar talk, GeometryTopology Seminar, University of Maryland, College Park, MD.
October 3, seminar talk, Topology Seminar, Oklahoma State University, Stillwater, OH.
September 2529, invited speaker, Symplectic Geometry, Low Dimensional Topology, and Quantum Fields, Clay Mathematics Institute, Oxford, UK.
February 69, plenary speaker, The Tenth East Asian School of Knots and Related Topics, Soochow University, Suzhou, China.
2022
April 69, invited speaker, AMS 2022 Joint Mathematics Meetings, Special Session on Skein Theory and Quantum Algebra, Washington State Convention Center, Seattle, WA.
March 22, seminar talk, Geometry/Topology Seminar, Rutgers University, New Brunswick, NJ.
March 15, seminar talk, Geometry and Topology Seminar, Michigan State University, East Lansing, MI.
2021
September 15, colloquium talk, Colloquium, Center of Mathematical Sciences and Applications, Harvard University, Cambridge MA.
March 25, seminar talk, Geometry and Topology Seminar, Chern Institute of Mathematics, Nankai University, Tianjin, China.
March 3, seminar talk, Topology Seminar, University of British Columbia, Vancouver, BC Canada.
2020
September 29, seminar talk, Geometry/Topology Seminar, Rutgers University, New Brunswick, NJ.
September 15, seminar talk, Geometry and Topology Seminar, Michigan State University, East Lansing, MI.
2019
December 1620, invited speaker, On Topological Quantum Computing, Shenzhen, China.
November 810, invited speaker, Texas Geometry and Topology Conference 2019, Texas A&M University, College Station, TX.
September 16, seminar talk, Geometry and Topology Seminar, University of Luxembourg, Luxembourg.
July 1620, invited speaker, In and around Topological Physics, Beijing International Center for Mathematical Research, Beijing, China.
June 914, 45Minute Lecture, The 8th International Congress of Chinese Mathematicians of 2019, Yau Mathematical Sciences Center (YMSC) of Tsinghua University and the Department of Mathematical Sciences of Tsinghua University, Beijing, China.
May 2731, invited speaker, Quantum Topology and Hyperbolic Geometry, Da Nang, Vietnam.
May 2224, invited speaker, Intelligence of Lowdimensional Topology 2019, RIMS, Kyoto University, Kyoto, Japan.
April 1314, invited speaker, AMS 2019 Spring Eastern Sectional Meeting , Special Session on Knot Theory, the Colored Jones Polynomial, and Khovanov Homology , University of Connecticut Hartford, Hartford, CT.
January 28, seminar talk, Geometry and Topology Seminar, University of Southern California, Los Angeles, CA.
January 22, seminar talk, Quantum Algebra/Topology Seminar, University of California, Santa Barbara, Santa Barbara, CA.
2018
December 1721, invited speaker, Classical and Quantum Threemanifold Topology, Monash University, Clayton campus, Melbourne, Australia.
November 9, seminar talk, Geometric Topology Seminar, Columbia University, New York, NY.
August 2426, invited speaker, Teichmuller Theory and Related Topics, Tsinghua University, Beijing, China.
July 913, invited speaker, Geometry, Quantum Topology and Asymptotics 2018, Sandbjerg Estate, Sønderborg, Denmark.
July 26, invited speaker, Geometry, Quantum Topology and Asymptotics 2018, Geneva, Switzerland.
March 19, seminar talk, Topology Seminar, The University of Texas at Austin, Austin, TX.
March 1116, contributed speaker, Modular Forms and Quantum Knot Invariants, Banff International Research Station, Banff, Canada.
2017
October 27, seminar talk, Geometry and Topology Seminar, California Institute of Technology, Pasadena, CA.
October 16, seminar talk, Geometry Seminar, Texas A&M University, College Station, TX.
October 6, seminar talk, Algebra and Combinatorics Seminar, Texas A&M University, College Station, TX.
September 1617, invited speaker, AMS 2017 Fall Eastern Sectional Meeting , Special Session on Knots, 3manifolds and their invariants, State University of New York at Buffalo, Buffalo, NY
September 910, invited speaker, AMS 2017 Fall Central Sectional Meeting, Special Session on Invariants of Links and 3Manifolds, University of North Texas, Denton, TX
August 612, invited speaker, GEometric structures And Representation varieties (GEAR Network), Third GEAR Retreat, Stanford University, Stanford, CA.
April 3, seminar talk, GeometryTopology Seminar, University of Maryland, College Park, MD.
February 6, colloquium talk, Colloquium, University of Hawaii at Manoa, Honolulu, HI.
January 30, colloquium talk, Colloquium, Louisiana State University, Baton Rouge, LA.
January 18, colloquium talk, Colloquium, Texas A&M University, College Station, TX.
2016
December 1819, invited speaker, 2016 Young Mathematican Forum, Beijing International Center for Mathematical Research, Beijing, China.
December 12, colloquium talk, Colloquium, Temple University, Philadelphia, PA.
December 9, seminar talk, Geometry Seminar, Texas A&M University, College Station, TX.
December 8, seminar talk, Groups and Dynamics Seminar, Texas A&M University, College Station, TX.
November 22, seminar talk, Geometry Seminar, University of Virginia, Charlottesville, VA.
November 8, seminar talk, Topology Seminar, University of Oregon, Eugene, OR
October 31, seminar talk, The Joint Los Angeles Topology Seminar, University of Southern California, Los Angeles, CA.
September 2425, invited speaker, AMS 2016 Fall Eastern Sectional Meeting, Special Session on Decomposing 3manifolds, Bowdoin College, Brunswick, ME.
July 2430, contributed speaker, Workshop on GrothendieckTeichmüller Theories, Chern Institute of Mathematics, Nankai University, Tianjin, China.
July 1723, contributed speaker, Knots in Hellas 2016, International Olympic Academy, Ancient Olympia, Greece.
June 1315, invited speaker, 2016 International Conference on Lowdimensional Topology, Southwest Jiaotong University, Chengdu, China.
April 13, seminar talk, Geometry and Topology Seminar, Michigan State University, East Lansing, MI.
March 1113, invited speaker, Advances in Quantum and LowDimensional Topology 2016, University of Iowa, Iowa City, IA.
March 10, colloquium talk, Mathematics Colloquium, Uinversity of Iowa, Iowa City, IA.
March 8, seminar talk, Baby Topology Seminar, Uinversity of Iowa, Iowa City, IA.
January 1115, invited speaker, Tsinghua Sanya International Mathematics Forum, Teichmuller Theory and Low Dimensional Topology, Yau Mathematical Sciences Center, Tsinghua University, Sanya, China.
January 8, seminar talk, Informal Geometry & Topology Seminar, Stanford University, Stanford, CA.
January 69, invited speaker, 2016 Joint Mathematics Meetings, Special Session on Topological Representation Theory, Washington State Convention Center, Seattle, WA.
2015
November 1415, invited speaker, AMS 2015 Fall Eastern Sectional Meeting, Special Session on Geometry of groups, surfaces and 3manifolds, Rutgers University, New Brunswick, NJ.
October 6, seminar talk, Topology Seminar and Station Q Seminar, University of California, Santa Barbara, Santa Barbara, CA.
October 5, seminar talk, Geometry and Topology Seminar, University of Southern California, Los Angeles, CA.
September 30, seminar talk, Topology Seminar, University of California, Berkeley, Berkeley, CA.
September 29, seminar talk, Geometry/Topology Seminar, University of California, Davis, Davis, CA.
September 15, seminar talk, Topology Seminar, Beijing University, Beijing, China.
August 1014, invited speaker, Invariants in Low Dimensional Geometry, Gazi University, Ankara, Turkey. The SLIDES of my talk.
July 2731, invited speaker, New Developments in TQFT, Center for Quantum Geometry and Moduli Spaces, Aarhus, Denmark. The VIDEO and SLIDES of my talk.
July 1522, invited speaker, First Encounter to Quantum Topology, Center for Mathematical Challenges (CMC), KIAS, Seoul, Korea. The VIDEOS 1 2 of my talk.
May 29, seminar talk, Geometry and Topology Seminar, California Institute of Technology, Pasadena, CA.
March 10, seminar talk, Topology/Geometry Seminar, Rutgers University, New Brunswick, NJ.
March 6, seminar talk, Geometry & Analysis Seminar, University of California, Santa Cruz, Santa Cruz, CA.
February 26, seminar talk, Topology Seminar, Oklahoma State University, Stillwater, OH.
January 2629, plenary speaker, The Tenth East Asian School of Knots and Related Topics, East China Normal University, Shanghai, China.
2014
August 2831, invited speaker, ChinaRussia Workshop on Knot Theory and Related Topics, Beijing International Center for Mathematical Research, Beijing, China.
April 25, seminar talk, Informal Geometry & Topology Seminar, Stanford University, Stanford, CA.
April 18, seminar talk, Informal Geometry & Topology Seminar, Stanford University, Stanford, CA.
March 24, seminar talk, Geometry Seminar, Purdue University, West Lafayette, IN.
March 14, seminar talk, Geometry and Topology Seminar, California Institute of Technology, Pasadena, CA.
2013
October 1820, invited speaker, AMS 2013 Fall Central Sectional Meeting, Special Session on Geometric Aspects of 3Manifold Invariants, Washington University, St. Louis, MO.
September 25, seminar talk, Topology Seminar, University of California, Berkeley, Berkeley, CA.
July 2931, invited speaker, 2013 Conference on Lowdimensional Topology, Liaoning Normal University, Dalian, Liaoning, China.
April 2628, contributed speaker, Workshop on Minimal Surfaces, 3Manifold Topology and Related Topics, Massachusetts Institute of Technology, Cambridge, MA.
February 19, seminar talk, Geometry/Topology Seminar, Rutgers University, New Brownswick, NJ.
February 12, seminar talk, Geometry/Topology Seminar, Rutgers University, New Brownswick, NJ.
January 912, invited speaker, AMS 2013 Joint Mathematics Meetings, Special Session on Geometric and Analytic Methods in Teichmuller Theory and Hyperbolic Geometry, San Diego Convention Center, San Diego, CA. The SLIDES of my talk.
2012
July 23August 3, junior speaker, GEometric structures And Representation varieties (GEAR Network), Junior Retreat 2012, University of Illinois in UrbanaChampaign, Urbana, IL. The VIDEO of my talk.
July 1518, invited speaker, 2012 Conference on Lowdimensional Topology, Fudan University, Shanghai, China.
May 2527, contributed speaker, 2012 Lehigh University Geometry and Topology Conference, Lehigh University, Bethlehem, PA.
February 7, seminar talk, Geometry and Topology Seminar, Graduate Center of CUNY, New York, NY.
January 24, seminar talk, GeometryTopology Seminar, Temple University, Philadelphia, PA.
2011
December 9, seminar talk, "A Deformation of Penner's Simplicial Coordinate," Complex Analysis and Dynamics Seminar, Graduate Center of CUNY, New York, NY.
December 24, Distinguished Graduate Student Speaker (50 minutes), Knots in Washington XXXIII, George Washington University, Washington DC. A POSTER of my talk.
November 4, seminar talk, "The Skein Algebra of Punctured Surfaces," Geometry and Topology Seminar, California Institute of Technology, Pasadena, CA.
November 2, seminar talk, Geometry and Topology Seminar, University of Southern California, Los Angeles, CA.
November 1, seminar talk, Topology Seminar, University of California, Santa Barbara, Santa Barbara, CA.
March 2427, invited speaker, The Triennial AhlforsBers Colloquium, Rice University, Houston, TX.
March 1416, invited speaker, "A Deformation of Penner's Coordinate of the Decorated Teichmuller Space," Graduate Student and PostDoc Workshop on Low Dimensional Topology and Geometry, Princeton University, Princeton, NJ.
2010
May 2223, invited speaker, "On the Hyperbolic Gluing Equations and Representations of Fundamental Groups of Closed $3$Manifolds," AMS 2010 Spring Eastern Sectional Meeting, Special Session on Invariants of Knots, Links, and 3Manifolds, Newark, NJ.
2007
December 810, invited speaker, "A BV structure on the Hochschild cohomology of truncated polynomials," CMS Winter 2007 Meeting, Homotopy Theory Session, The University of Western Ontario, London, Ontario, Canada.
Minicourses:
Fall 2018, Math 689: Special Topics in Quantum Topology.
Spring 2016, Math28401: Topics in Geometric Topology.
August 24September 18, 2015, Summer Course, Mathematical Sciences Center, Tsinghua University, Beijing, China. The NOTES of my lectures.
July 17August 14, 2014, Summer Course, Mathematical Sciences Center, Tsinghua University, Beijing, China.
July 1526, 2013 Summer School on Lowdimensional Topology, Liaoning Normal University, Dalian, Liaoning, China.
July 812 and August 59, 2013, Summer School for Topnotch Undergraduate Students, Fudan University, Shanghai, China.
July 813, 2012 Workshop on Lowdimensional Topology, Soochow University, Suzhou, Jiangsu, China. The notes 1, 2, 3, 4 of my lectures.