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FMSP Lectures
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
Seminar information archive
2015/01/27
13:00-16:20 Room #126 (Graduate School of Math. Sci. Bldg.)
Frédéric Abergel (École Centrale Paris)
Limit order books II
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
Frédéric Abergel (École Centrale Paris)
Limit order books II
[ Abstract ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ Reference URL ]In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
2015/01/26
12:30-13:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Peter Trapa (University of Utah)
Unitary representations of reductive Lie groups III
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
Peter Trapa (University of Utah)
Unitary representations of reductive Lie groups III
[ Abstract ]
Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
[ Reference URL ]Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
2015/01/26
9:30-10:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Benjamin Harris (Oklahoma State University)
The Geometry of Nontempered Characters
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
Benjamin Harris (Oklahoma State University)
The Geometry of Nontempered Characters
[ Abstract ]
In this talk, we will survey the results of Rossmann and Schmid-Vilonen on geometric formulas for nontempered characters of reductive groups, and we will mention an old result of Barbasch-Vogan on the special case A_q(lambda). We will discuss what nontempered character formulas would be necessary to generalize the main formula of the second talk, and we will make conjectures.
[ Reference URL ]In this talk, we will survey the results of Rossmann and Schmid-Vilonen on geometric formulas for nontempered characters of reductive groups, and we will mention an old result of Barbasch-Vogan on the special case A_q(lambda). We will discuss what nontempered character formulas would be necessary to generalize the main formula of the second talk, and we will make conjectures.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
2015/01/26
13:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Frédéric Abergel (École Centrale Paris)
Limit order books I
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
Frédéric Abergel (École Centrale Paris)
Limit order books I
[ Abstract ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ Reference URL ]In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
2015/01/26
11:00-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Raul Gomez (Cornell University)
Local Theta lifting of generalized Whittaker models.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
Raul Gomez (Cornell University)
Local Theta lifting of generalized Whittaker models.
[ Abstract ]
In this talk, we describe the behavior of the space of generalized Whittaker models attached to a nilpotent orbit under the local theta correspondence. This description is a generalization of a result of Moeglin in the p-adic setting. This is joint work with Chengbo Zhu.
[ Reference URL ]In this talk, we describe the behavior of the space of generalized Whittaker models attached to a nilpotent orbit under the local theta correspondence. This description is a generalization of a result of Moeglin in the p-adic setting. This is joint work with Chengbo Zhu.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
2015/01/25
12:30-13:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Peter Trapa (University of Utah)
Unitary representations of reductive Lie groups II
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
Peter Trapa (University of Utah)
Unitary representations of reductive Lie groups II
[ Abstract ]
Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
[ Reference URL ]Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
2015/01/25
11:00-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Benjamin Harris (Oklahoma State University)
The Geometry of Harmonic Analysis
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
Benjamin Harris (Oklahoma State University)
The Geometry of Harmonic Analysis
[ Abstract ]
In this talk, we will present recent joint work with Tobias Weich. When G is a real, reductive algebraic group and X is a homogeneous space for G with an invariant measure, we will completely describe the regular, semisimple asymptotics of the support of the Plancherel measure for L^2(X). We will give concrete examples of this theorem, describing what can and cannot be deduced from this result.
[ Reference URL ]In this talk, we will present recent joint work with Tobias Weich. When G is a real, reductive algebraic group and X is a homogeneous space for G with an invariant measure, we will completely describe the regular, semisimple asymptotics of the support of the Plancherel measure for L^2(X). We will give concrete examples of this theorem, describing what can and cannot be deduced from this result.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
2015/01/25
9:30-10:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Raul Gomez (Cornell University)
Generalized and degenerate Whittaker models associated to nilpotent orbits.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
Raul Gomez (Cornell University)
Generalized and degenerate Whittaker models associated to nilpotent orbits.
[ Abstract ]
In this talk, we examine the relation between the different spaces of Whittaker models that can be attached to a nilpotent orbit. We will also explore their relation to other nilpotent invariants (like the wave front set) and show some examples and applications.
This is joint work with Dmitry Gourevitch and Siddhartha Sahi.
[ Reference URL ]In this talk, we examine the relation between the different spaces of Whittaker models that can be attached to a nilpotent orbit. We will also explore their relation to other nilpotent invariants (like the wave front set) and show some examples and applications.
This is joint work with Dmitry Gourevitch and Siddhartha Sahi.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
2015/01/24
13:00-14:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Peter Trapa (University of Utah)
Unitary representations of reductive Lie groups I
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
Peter Trapa (University of Utah)
Unitary representations of reductive Lie groups I
[ Abstract ]
Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
[ Reference URL ]Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
2015/01/24
16:30-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Benjamin Harris (Oklahoma State University)
The Geometry of Tempered Characters
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
Benjamin Harris (Oklahoma State University)
The Geometry of Tempered Characters
[ Abstract ]
In this introductory talk, we will briefly recall parts of Harish-Chandra's theory of characters for reductive groups and the geometric formula of Rossmann and Duflo for tempered characters of reductive groups. Examples will be given in the case G=SL(2,R).
[ Reference URL ]In this introductory talk, we will briefly recall parts of Harish-Chandra's theory of characters for reductive groups and the geometric formula of Rossmann and Duflo for tempered characters of reductive groups. Examples will be given in the case G=SL(2,R).
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
2015/01/24
14:30-15:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Raul Gomez (Cornell University)
The Tor and Ext functors for smooth representations of real algebraic groups.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
Raul Gomez (Cornell University)
The Tor and Ext functors for smooth representations of real algebraic groups.
[ Abstract ]
Inspired by the recent work of Dipendra Prasad in the $p$-adic setting, we define the Tor and Ext functors for an appropriate category of smooth representations of a real algebraic group $G$, and give some applications. This is joint work with Birgit Speh.
[ Reference URL ]Inspired by the recent work of Dipendra Prasad in the $p$-adic setting, we define the Tor and Ext functors for an appropriate category of smooth representations of a real algebraic group $G$, and give some applications. This is joint work with Birgit Speh.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
2014/12/10
16:00-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / Univ. Paris-Sud)
Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium
Danielle Hilhorst (CNRS / Univ. Paris-Sud)
Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium
[ Abstract ]
This talk is concerned with a mathematical model for the storage of radioactive waste. The model which we study deals with the diffusion of chemical species transported by water, with possible dissolution or precipitation and for a rather general kinetics law. In this talk, we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by the combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case. This is joint work with Hideki Murakawa.
This talk is concerned with a mathematical model for the storage of radioactive waste. The model which we study deals with the diffusion of chemical species transported by water, with possible dissolution or precipitation and for a rather general kinetics law. In this talk, we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by the combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case. This is joint work with Hideki Murakawa.
2014/11/10
17:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Alfred Ramani (Ecole Polytechnique)
Discrete Painlevé equations with periodic coefficients (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani.pdf
Alfred Ramani (Ecole Polytechnique)
Discrete Painlevé equations with periodic coefficients (ENGLISH)
[ Abstract ]
We present a series of results on discrete Painlevé equations with coefficients which are periodic functions of the independent variable. We show by explicit construction that for each affine Weyl group there exists an equation the coefficients of which have maximal periodicity. New results on equations associated to the affine Weyl group E_8 are also presented.
[ Reference URL ]We present a series of results on discrete Painlevé equations with coefficients which are periodic functions of the independent variable. We show by explicit construction that for each affine Weyl group there exists an equation the coefficients of which have maximal periodicity. New results on equations associated to the affine Weyl group E_8 are also presented.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani.pdf
2014/09/19
14:30-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Victoria Lebed (Osaka City University, JSPS)
A bridge between knotted graphs and axiomatizations of groups (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Lebed.pdf
Victoria Lebed (Osaka City University, JSPS)
A bridge between knotted graphs and axiomatizations of groups (ENGLISH)
[ Abstract ]
This talk will be devoted to a new algebraic structure called qualgebra. From the topological viewpoint, our construction is motivated by a study of knotted 3-valent graphs via combinatorially defined coloring invariants. From the algebraic viewpoint, it gives a part of an alternative axiomatization of groups, describing the properties of the conjugation operation and its interactions with the group multiplication. Explicit examples of qualgebras and associated graph invariants will be given.
[ Reference URL ]This talk will be devoted to a new algebraic structure called qualgebra. From the topological viewpoint, our construction is motivated by a study of knotted 3-valent graphs via combinatorially defined coloring invariants. From the algebraic viewpoint, it gives a part of an alternative axiomatization of groups, describing the properties of the conjugation operation and its interactions with the group multiplication. Explicit examples of qualgebras and associated graph invariants will be given.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Lebed.pdf
2014/09/12
10:30-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Hung V. Tran (The University of Chicago)
Stochastic homogenization for first order Hamilton-Jacobi equations(III) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf
Hung V. Tran (The University of Chicago)
Stochastic homogenization for first order Hamilton-Jacobi equations(III) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf
2014/09/10
10:30-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Hung V. Tran (The University of Chicago)
Stochastic homogenization for first order Hamilton-Jacobi equations(II) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf
Hung V. Tran (The University of Chicago)
Stochastic homogenization for first order Hamilton-Jacobi equations(II) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf
2014/09/09
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hatem Zaag (CNRS/University of Paris Nord)
Energy methods and blow-up rate for semilinear wave equations in the superconformal case (ENGLISH)
Hatem Zaag (CNRS/University of Paris Nord)
Energy methods and blow-up rate for semilinear wave equations in the superconformal case (ENGLISH)
[ Abstract ]
In a series of papers with Mohamed Ali Hamza (University of Tunis-el Manar), we consider the semilinear wave equations with power nonlinearity.
In the subconformal and the conformal case, we consider perturbations with lower order terms and modify the Lyapunov functional Antonini and Merle designed for the unperturbed case. We also find a blow-up criterion for the equation. As a consequence, we bound the Lyapunov functional. Thanks to interpolations in Sobolev spaces and a Gagliardo-Nirenberg inequality, we bound the solution in the self-similar variable, which gives a sharp bound on the blow-up rate.
Surprisingly, our approach works in the superconformal case (still Sobolev subcritical), leading to a new bound on the blow-up rate, which improves the bound of Killip, Stoval and Visan.
In a series of papers with Mohamed Ali Hamza (University of Tunis-el Manar), we consider the semilinear wave equations with power nonlinearity.
In the subconformal and the conformal case, we consider perturbations with lower order terms and modify the Lyapunov functional Antonini and Merle designed for the unperturbed case. We also find a blow-up criterion for the equation. As a consequence, we bound the Lyapunov functional. Thanks to interpolations in Sobolev spaces and a Gagliardo-Nirenberg inequality, we bound the solution in the self-similar variable, which gives a sharp bound on the blow-up rate.
Surprisingly, our approach works in the superconformal case (still Sobolev subcritical), leading to a new bound on the blow-up rate, which improves the bound of Killip, Stoval and Visan.
2014/09/08
10:30-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Hung V. Tran (The University of Chicago)
Stochastic homogenization for first order Hamilton-Jacobi equations(I) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf
Hung V. Tran (The University of Chicago)
Stochastic homogenization for first order Hamilton-Jacobi equations(I) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf
2014/07/11
15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State Univ.)
Conditional stability estimate for the Calderon's problem in two dimensional case (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov140711.pdf
Oleg Emanouilov (Colorado State Univ.)
Conditional stability estimate for the Calderon's problem in two dimensional case (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov140711.pdf
2014/07/03
16:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)
Gordan Savin (Univ. of Utah)
Structure of rational orbits in prehomogeneous spaces. (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Savin.pdf
Gordan Savin (Univ. of Utah)
Structure of rational orbits in prehomogeneous spaces. (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Savin.pdf
2014/05/15
16:30-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)
Cédric Villani (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature ― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/Villani.html
Cédric Villani (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature ― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/Villani.html
2014/01/15
14:50-16:20 Room #056 (Graduate School of Math. Sci. Bldg.)
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory IV (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory IV (ENGLISH)
[ Abstract ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ Reference URL ]Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf
2014/01/14
14:50-16:20 Room #056 (Graduate School of Math. Sci. Bldg.)
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory III (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory III (ENGLISH)
[ Abstract ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ Reference URL ]Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf
2014/01/10
14:50-16:20 Room #056 (Graduate School of Math. Sci. Bldg.)
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory II (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory II (ENGLISH)
[ Abstract ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ Reference URL ]Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf
2014/01/09
14:50-16:20 Room #056 (Graduate School of Math. Sci. Bldg.)
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory I (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory I (ENGLISH)
[ Abstract ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ Reference URL ]Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf
