Ivan Ip's Homepage

Publications

Talks and Presentations

Conferences

Research Talks Presented:

Year	Conference and Seminar	Title (click for abstract)
2024 Dec	The theory of cluster algebras and its applications, 14th AIMS Conference, NYU Abu Dhabi	Casimir Actions of Parabolic Positive Representations
2024 Jan	Physical Mathematics and Beyond Workshop, KIAS, South Korea	Regular Positive Representations
2023 Sept	Workshop on cluster algebras representation theory and algebraic geometry, Hong Kong University	Regular Positive Representations
2023 July	Workshop on Representation Theory and Topology and Their Application in Related Science and Technology, Xinjiang University	Regular Positive Representations
2023 Mar	Advances in Cluster Algebras 2023, Japan	Regular Positive Representations
2023 Mar	Lunch Time Seminar, Sun Yat-sen University	Regular Positive Representations
2022 Apr	Geometry, Representation Theory, and Physics Seminar Yale University	Parabolic Positive Representations of Real Quantum Groups
2022 Feb	Quantum Groups and Cluster Algebras, QSMS, Korea,	Positive Representations at Zero Casimirs
2021 Mar	Online School: Quantum Geometry and Represenation Theory	Positive Representations of Split Real Quantum Groups
2021 Mar	Geometry, Number Theory, and Representation Theory Seminar, University of Alberta	Parabolic Positive Representations
2020 Nov	2020 Symposium on Representation Theory, Japan	Parabolic Positive Representations
2020 Oct	Recent advances in combinatorial representation theory, RIMS, Kyoto University	Parabolic Positive Representations
2019 Nov	HKUST-KAIST-NUS Joint Workshop in Mathematics, National University of Singapore	Positive Peter-Weyl Theorem
2019 July	Workshop on Classical Quantum Integrable System (CQIS2019), Euler Institute, St. Petersburg	Positive Peter-Weyl Theorem
2019 June	Cluster Algebra 2019 (CA19), RIMS, Kyoto University	Positive Peter-Weyl Theorem
2019 June	ICCM 2019, Tsinghua University	Positive Peter-Weyl Theorem
2019 Mar	MAXIMALS Algebra Seminar, Edinburgh University	Positive Peter-Weyl Theorem
2018 Nov	Workshop on Crystal Bases, Cluster Algebras, and Poisson Geometry, Hong Kong University	Cluster realization of tensor product decomposition of positive representations
2018 Nov	"Introduction to Modern Mathematics" Series Colloquium, Yau Mathematical Sciences Center of Tsinghua University	Generalized Teichmüller theory, spin structures, and Ptolemy relations
2018 May	Representation Theory Seminar, RIMS, Kyoto University	Positive Peter-Weyl Theorem
2018 Mar	MathPhys 2018, Rikkyo University	Cluster realization and tensor product decomposition of positive representations
2017 Nov	Infinite Analysis 17, Osaka City University	Cluster realization and tensor product decomposition of positive representation
2017 Sept	Mathematics Society of Japan Autumn Meeting 2017	On tensor product decomposition of positive representations
2017 July	Workshop on Representation Theory of Lie Superalgebras and Related Topics, Taipei	Generalized Teichm ü ller Spaces, Spin Structures, and Ptolemy Transformations
2017 July	Workshop on Classical and Quantum Integrable Systems, Dubna	Positive representations and cluster realization of quantum groups
2017 May	Scientific Seminar, Perimeter Institute	Positive Representations of Split Real Quantum Groups (Video)
2017 Apr	Geometric Representation Theory Seminar, University of Toronto	Positive Representations of Split Real Quantum Groups
2017 Mar	Mathematics Society of Japan Spring Meeting 2017 (特別講演)	Positive representations and cluster realization of quantum groups
2017 Mar	Mathematics of Superstring Theory, Kavli IPMU	N = 2 Super Teichm ü ller theory
2017 Feb	KTGU Workshop, Kyoto University	Cluster realization of Uq(g) and factorization of universal R matrix
2017 Jan	Representation Theory Seminar, RIMS, Kyoto University	Cluster realization of Uq(g) and factorization of universal R matrix
2016 Dec	Mathematics Colloqium, HKUST	Positive representations of split real quantum groups
2016 Nov	Kyoto Operator Algebra Seminar, Kyoto University	Positive representations: a bridge between Drinfeld-Jimbo quantum group and C*-algebra
2016 Sept	Mathematics Society of Japan Autumn Meeting 2016	Positive representations of split real quantum groups
2016 June	The 24^th International Conference on Integrable Systems and Quantum symmetries, Prague	Split Real Quantum Groups
2016 May	Mathematical Physics and Geometric Analysis Seminar, KIAS, Seoul	Positive Casimir and Central Characters of Split Real Quantum Groups
2016 Mar	Columbia Symplectic Geometry, Gauge Theory, and Categorification Seminar, Columbia University	Positive Casimir and Central Characters of Split Real Quantum Groups
2016 Mar	Geometry, Symmetry and Physics Seminar, Yale University	Positive Casimir and Central Characters of Split Real Quantum Groups
2015 Sep	Geometry Seminar, HKU, Hong Kong	Quantum dilogarithm identities at root of unity
2015 July	Seminar on Pure Mathematics, HKUST, Hong Kong	Quantum dilogarithm identities at root of unity
2014 July	RIMS Project 2014 on Geometric Representation Theory, Kyoto	Positive Representations and Quantum Higher Teichmüller Theory
2014 July	Summer School on Quantum Groups and Integrability, University of Hamburg	Positive Representations and Quantum Higher Teichmüller Theory
2014 July	The 30^th International Colloquium on Group-Theoretical Methods in Physics, Ghent University	Positive Representations and Quantum Higher Teichmüller Theory
2014 July	International Conference "Mathematics Days in Sofia"	Positive Representations and Quantum Higher Teichmüller Theory
2014 Jan	Conformal Block Seminar, IPMU	Quantum Liouville's Theory and Modular Double of Uq(sl(2,R))
2013 Dec	Algebra/Geometry/Topology Seminar, University of Melbourne	Positive Representations of Split Real Quantum Groups
2013 Nov	Infinite Analysis 13 Autumn School on Quantum Dilogarithm, Modular Double, and Representation Theory, Osaka City University	Positive Representations: Motivation, Construction and Braiding Structure
2013 Sept	String Lunch, IPMU	Quantum Teichmüller Theory and Liouville's Theory
2013 July	String Theory, Integrable Systems and Representation theory, RIMS, Kyoto	Braiding Structure of Positive Representation of Split Real Quantum Groups
2013 July	Representation Theory Seminar, KIAS, Seoul	Positive Representations: Motivation, Construction and Perspective from C* Algebra
2013 Apr	Seminar on Geometric Representation Theory and Quantum Integrable System, University of Tokyo	Positive Representations: Motivation, Construction and Braiding Structure
2013 Apr	String Lunch, IPMU	Positive Grassmannian and Scattering Amplitudes
2013 Mar	Math Get-together Seminar, IPMU	Universal R-operator for split real quantum groups
2013 Mar	Infinite Analysis: Past, Present and Future, Kyoto University	Positive representations of split real quantum group
2013 Feb	Lie Theory Seminar, HKUST	Positive representations of split real quantum group
2013 Feb	Geometry, Symmetry and Physics Seminar, Yale	Universal R-operator for split real quantum groups
2013 Jan	Informal Mathematical Physics Seminar, Columbia University	Positive representations of split real quantum group
2012 Nov	Mathematics and Physics Seminar, Rikkyo University	Positive representations of split real quantum group
2012 Sept	Math-String Seminar, IPMU	Positive representations of split real quantum groups
2012 Aug	The 29^th International Colloquium on Group-Theoretical Methods in Physics, Chern Institute	Positive representations of split real quantum group
2012 Apr	Geometry, Symmetry and Physics Seminar, Yale	Positive representations of split real quantum group
2011 Oct	Workshop in Master Class, QGM, Aarhus	Positive representations of split real quantum group
2011 Feb	Graduate Student Seminar, Yale	The Yang Baxter equation and quantum double construction
2010 Feb	Graduate Student Seminar, Yale	Special functions in representation theory
2008 Dec	Graduate Student Seminar, Yale	The mysterious dilogarithm (slides)
2007 Nov	Graduate Student Seminar, Yale	What is noncommutative geometry?

Other Course Projects:

My Yale Course Projects and Presentations:

Year	Title	Instructor
2010	The Core of an N person Game	G. Kalai
2010	On the Vassiliev Knot Invariant	A. Lachowska
2009	A Review of Symmetries of Rotating Black Holes	V. Moncreif
2009	A Model of Homotopy Theory of Homotopy Theories	D. Borisov
2009	Modular Double and Tensor Product Representation of U_q(sl(2,R))	I. Frenkel
2006	A Brief Introduction to Sheaf Cohomology	A. Marian
2006	A Homological Approach to Two Problems on Finite Set	G. Kalai
2006	Representation Theory of SL₂(R)	I. Frenkel

My Undergraduate Research Projects:

Year	Title	Instructor
2005	Geometry and Invariance of Kernel Based Method	T.Y. Kwok, HKUST
2005	Target Driven Smoke Animation	C.L. Tai, HKUST
2005	Elliptic Curves, Modular Forms and Hecke Operators	Y. Zhu, HKUST
2004	Lie Derivatives and Cartan's Magic Formula	O. Radko, UCLA
2003	Application of Genetic Algorithm on Stock Market Forecasting	K.Y. Szeto, HKUST
2003	Chaos Theory and Fractals: Mandelbrot Set and Julia Set	M. Wong, HKUST