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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Kensuke Ishitani (Graduate School of Science and Engineering, Tokyo Metropolitan University)
Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals (JAPANESE)
Kensuke Ishitani (Graduate School of Science and Engineering, Tokyo Metropolitan University)
Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals (JAPANESE)
[ Abstract ]
In this presentation, we present a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples.
In this presentation, we present a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples.
2017/06/14
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yongquan Hu (Chinese Academy of Sciences, Morningside Center of Mathematics)
Multiplicity one for the mod p cohomology of Shimura curves (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~t-saito/title_Hu.pdf
Yongquan Hu (Chinese Academy of Sciences, Morningside Center of Mathematics)
Multiplicity one for the mod p cohomology of Shimura curves (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~t-saito/title_Hu.pdf
2017/06/13
Numerical Analysis Seminar
16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Hirofumi Notsu (Kanazawa University)
Numerical analysis of viscoelastic fluid models (Japanese)
Hirofumi Notsu (Kanazawa University)
Numerical analysis of viscoelastic fluid models (Japanese)
[ Abstract ]
Numerical methods for viscoelastic fluid models are studied. In viscoelastic fluid models the stress tensor is often written as a sum of the viscous stress tensor depending linearly on the strain rate tensor and the extra stress tensor for the viscoelastic contribution. In order to describe the viscoelastic contribution another equation for the extra stress tensor is required. In the talk we mainly deal with the Oldroyd-B and the Peterlin models among several proposed viscoelastic fluid models, and present error estimates of finite element schemes based on the method of characteristics. The key issue in the estimates is the treatment of the divergence of the extra stress tensor appearing in the equation for the velocity and the pressure.
Numerical methods for viscoelastic fluid models are studied. In viscoelastic fluid models the stress tensor is often written as a sum of the viscous stress tensor depending linearly on the strain rate tensor and the extra stress tensor for the viscoelastic contribution. In order to describe the viscoelastic contribution another equation for the extra stress tensor is required. In the talk we mainly deal with the Oldroyd-B and the Peterlin models among several proposed viscoelastic fluid models, and present error estimates of finite element schemes based on the method of characteristics. The key issue in the estimates is the treatment of the divergence of the extra stress tensor appearing in the equation for the velocity and the pressure.
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Noboru Ogawa (Tokai University)
Local criteria for non-embeddability of Levi-flat manifolds (JAPANESE)
Noboru Ogawa (Tokai University)
Local criteria for non-embeddability of Levi-flat manifolds (JAPANESE)
[ Abstract ]
In this talk, we consider the Levi-flat embedding problem. Barrett showed that a smooth Reeb foliation on S^3 cannot be realized as a Levi-flat hypersurface in any complex surfaces. To do this, he focused the relationship between the holonomy along the compact leaf and a system of its defining functions. We will show a new criterion for non-embeddability of Levi-flat manifolds. Our result is a higher dimensional analogue of Barrett's theorem. In particular, this enables us to weaken the compactness assumption. For this purpose, we pose a partial generalization of Ueda theory on the analytic neighborhood structure of complex hypersurfaces. This talk is based on a joint work with Takayuki Koike (Kyoto University).
In this talk, we consider the Levi-flat embedding problem. Barrett showed that a smooth Reeb foliation on S^3 cannot be realized as a Levi-flat hypersurface in any complex surfaces. To do this, he focused the relationship between the holonomy along the compact leaf and a system of its defining functions. We will show a new criterion for non-embeddability of Levi-flat manifolds. Our result is a higher dimensional analogue of Barrett's theorem. In particular, this enables us to weaken the compactness assumption. For this purpose, we pose a partial generalization of Ueda theory on the analytic neighborhood structure of complex hypersurfaces. This talk is based on a joint work with Takayuki Koike (Kyoto University).
2017/06/12
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (Osaka University)
On Sp(2)-invariant asymptotically complex hyperbolic Einstein metrics on the 8-ball
Yoshihiko Matsumoto (Osaka University)
On Sp(2)-invariant asymptotically complex hyperbolic Einstein metrics on the 8-ball
[ Abstract ]
Following a pioneering work of Pedersen, Hitchin studied SU(2)-invariant asymptotically real/complex hyperbolic (often abbreviated as AH/ACH) solution to the Einstein equation on the 4-dimensional unit open ball. We discuss a similar problem on the 8-ball, on which the quaternionic unitary group Sp(2) acts naturally, focusing on ACH solutions rather than AH ones. The Einstein equation is treated as an asymptotic Dirichlet problem, and the Dirichlet data are Sp(2)-invariant “partially integrable” CR structures on the 7-sphere. A remarkable point is that most of such structures are actually non-integrable. I will present how we can practically compute the formal series expansion of the Einstein ACH metric corresponding to a given Dirichlet data, that is, an invariant partially integrable CR structure on the sphere.
Following a pioneering work of Pedersen, Hitchin studied SU(2)-invariant asymptotically real/complex hyperbolic (often abbreviated as AH/ACH) solution to the Einstein equation on the 4-dimensional unit open ball. We discuss a similar problem on the 8-ball, on which the quaternionic unitary group Sp(2) acts naturally, focusing on ACH solutions rather than AH ones. The Einstein equation is treated as an asymptotic Dirichlet problem, and the Dirichlet data are Sp(2)-invariant “partially integrable” CR structures on the 7-sphere. A remarkable point is that most of such structures are actually non-integrable. I will present how we can practically compute the formal series expansion of the Einstein ACH metric corresponding to a given Dirichlet data, that is, an invariant partially integrable CR structure on the sphere.
Algebraic Geometry Seminar
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Ivan Cheltsov (The University of Edinburgh)
Rational and irrational singular quartic threefolds (English)
Ivan Cheltsov (The University of Edinburgh)
Rational and irrational singular quartic threefolds (English)
[ Abstract ]
Burkhardt and Igusa quartics admit a faithful action of the symmetric group of degree 6.
There are other quartic threefolds with this property. All of them are singular.
Beauville proved that all but four of them are irrational. Burkhardt and Igusa quartics are known to be rational.
Two constructions of Todd imply the rationality of the remaining two quartic threefolds.
In this talk, I will give an alternative proof of both these (irrationality and rationality) results.
This proof is based on explicit small resolutions of the so-called Coble fourfold.
This fourfold is the double cover of the four-dimensional projective space branched over Igusa quartic.
This is a joint work with Sasha Kuznetsov and Costya Shramov.
Burkhardt and Igusa quartics admit a faithful action of the symmetric group of degree 6.
There are other quartic threefolds with this property. All of them are singular.
Beauville proved that all but four of them are irrational. Burkhardt and Igusa quartics are known to be rational.
Two constructions of Todd imply the rationality of the remaining two quartic threefolds.
In this talk, I will give an alternative proof of both these (irrationality and rationality) results.
This proof is based on explicit small resolutions of the so-called Coble fourfold.
This fourfold is the double cover of the four-dimensional projective space branched over Igusa quartic.
This is a joint work with Sasha Kuznetsov and Costya Shramov.
2017/06/06
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Chen Jiang (IPMU)
Fano varieties: K-stability and boundedness (English)
https://sites.google.com/site/chenjiangmath/
Chen Jiang (IPMU)
Fano varieties: K-stability and boundedness (English)
[ Abstract ]
There are two interesting problems for Fano varieties, K-stability and boundedness.
Significant progress has been made for both problems recently.
In this talk, I will show the boundedness of K-semistable Fano varieties with anti-canonical degree bounded from below, by using methods from birational geometry.
[ Reference URL ]There are two interesting problems for Fano varieties, K-stability and boundedness.
Significant progress has been made for both problems recently.
In this talk, I will show the boundedness of K-semistable Fano varieties with anti-canonical degree bounded from below, by using methods from birational geometry.
https://sites.google.com/site/chenjiangmath/
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Shunsuke Tsuji (The University of Tokyo)
A formula for the action of Dehn twists on the HOMFLY-PT type skein algebra and its application (JAPANESE)
Shunsuke Tsuji (The University of Tokyo)
A formula for the action of Dehn twists on the HOMFLY-PT type skein algebra and its application (JAPANESE)
[ Abstract ]
We give an explicit formula for the action of the Dehn twist along a simple closed curve of a surface on the completed HOMFLY-PT type skein modules of the surface in terms of the action of the completed HOMFLY-PT type skein algebra of the surface. As an application, using this formula, we construct an invariant for an integral homology 3-sphere which is an element of Q[ρ] [[h]].
We give an explicit formula for the action of the Dehn twist along a simple closed curve of a surface on the completed HOMFLY-PT type skein modules of the surface in terms of the action of the completed HOMFLY-PT type skein algebra of the surface. As an application, using this formula, we construct an invariant for an integral homology 3-sphere which is an element of Q[ρ] [[h]].
2017/06/01
Classical Analysis
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Akishi Ikeda (IPMU, University of Tokyo)
Homological and monodromy representations of framed braid groups
(JAPANESE)
Akishi Ikeda (IPMU, University of Tokyo)
Homological and monodromy representations of framed braid groups
(JAPANESE)
2017/05/31
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ryotaro Sakamoto (University of Tokyo)
Stark Systems over Gorenstein Rings (JAPANESE)
Ryotaro Sakamoto (University of Tokyo)
Stark Systems over Gorenstein Rings (JAPANESE)
2017/05/30
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Takayuki Morifuji (Keio University)
On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)
Takayuki Morifuji (Keio University)
On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)
[ Abstract ]
The hyperbolic torsion polynomial is defined to be the twisted Alexander polynomial associated to the holonomy representation of a hyperbolic knot. Dunfield, Friedl and Jackson conjecture that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjecture and explain its generalization to hyperbolic links.
The hyperbolic torsion polynomial is defined to be the twisted Alexander polynomial associated to the holonomy representation of a hyperbolic knot. Dunfield, Friedl and Jackson conjecture that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjecture and explain its generalization to hyperbolic links.
Infinite Analysis Seminar Tokyo
17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Soichi Okada (Graduate School of Mathematics, Nagoya University)
$Q$-functions associated to the root system of type $C$ (JAPANESE)
Soichi Okada (Graduate School of Mathematics, Nagoya University)
$Q$-functions associated to the root system of type $C$ (JAPANESE)
[ Abstract ]
Schur $Q$-functions are a family of symmetric functions introduced
by Schur in his study of projective representations of symmetric
groups. They are obtained by putting $t=-1$ in the Hall-Littlewood
functions associated to the root system of type $A$. (Schur
functions are the $t=0$ specialization.) This talk concerns
symplectic $Q$-functions, which are obtained by putting $t=-1$
in the Hall-Littlewood functions associated to the root system
of type $C$. We discuss several Pfaffian identities as well
as a combinatorial description for them. Also we present some
positivity conjectures.
Schur $Q$-functions are a family of symmetric functions introduced
by Schur in his study of projective representations of symmetric
groups. They are obtained by putting $t=-1$ in the Hall-Littlewood
functions associated to the root system of type $A$. (Schur
functions are the $t=0$ specialization.) This talk concerns
symplectic $Q$-functions, which are obtained by putting $t=-1$
in the Hall-Littlewood functions associated to the root system
of type $C$. We discuss several Pfaffian identities as well
as a combinatorial description for them. Also we present some
positivity conjectures.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Masaru Nagaoka (The University of Tokyo)
Contractible affine threefolds in smooth Fano threefolds (English or Japanese)
Masaru Nagaoka (The University of Tokyo)
Contractible affine threefolds in smooth Fano threefolds (English or Japanese)
[ Abstract ]
By the contribution of M. Furushima, N. Nakayama, Th. Peternell and M.
Schneider, it is completed to classify all projective compactifications
of the affine $3$-space $\mathbb{A}^3$ with Picard number one.
As a similar question, T. Kishimoto raised the problem to classify all
triplets $(V, U, D_1 \cup D_2)$ which consist of smooth Fano threefolds
$V$ of Picard number two, contractible affine threefolds $U$ as open
subsets of $V$, and the complements $D_1 \cup D_2 =V \setminus U$.
He also solved this problem when the log canonical divisors $K_V+D_1+D_2
$ are not nef.
In this talk, I will discuss the triplets $(V, U, D_1 \cup D_2)$ whose
log canonical divisors are linearly equivalent to zero.
I will also explain how to determine all Fano threefolds $V$ which
appear in such triplets.
By the contribution of M. Furushima, N. Nakayama, Th. Peternell and M.
Schneider, it is completed to classify all projective compactifications
of the affine $3$-space $\mathbb{A}^3$ with Picard number one.
As a similar question, T. Kishimoto raised the problem to classify all
triplets $(V, U, D_1 \cup D_2)$ which consist of smooth Fano threefolds
$V$ of Picard number two, contractible affine threefolds $U$ as open
subsets of $V$, and the complements $D_1 \cup D_2 =V \setminus U$.
He also solved this problem when the log canonical divisors $K_V+D_1+D_2
$ are not nef.
In this talk, I will discuss the triplets $(V, U, D_1 \cup D_2)$ whose
log canonical divisors are linearly equivalent to zero.
I will also explain how to determine all Fano threefolds $V$ which
appear in such triplets.
2017/05/29
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroshi Sawai (National Institute of Technology, Numazu College)
LCK structures on compact solvmanifolds
Hiroshi Sawai (National Institute of Technology, Numazu College)
LCK structures on compact solvmanifolds
[ Abstract ]
A locally conformal Kähler (in short LCK) manifold is said to be Vaisman if Lee form is parallel with respect to Levi-Civita connection. In this talk, we prove that a Vaisman structure on a compact solvmanifolds depends only on the form of the fundamental 2-form, and it do not depends on a complex structure. As an application, we give the structure theorem for Vaisman (completely solvable) solvmanifolds and LCK nilmanifolds. Moreover, we show the existence of LCK solvmanifolds without Vaisman structures.
A locally conformal Kähler (in short LCK) manifold is said to be Vaisman if Lee form is parallel with respect to Levi-Civita connection. In this talk, we prove that a Vaisman structure on a compact solvmanifolds depends only on the form of the fundamental 2-form, and it do not depends on a complex structure. As an application, we give the structure theorem for Vaisman (completely solvable) solvmanifolds and LCK nilmanifolds. Moreover, we show the existence of LCK solvmanifolds without Vaisman structures.
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Yusuke Isono (RIMS, Kyoto Univ.)
On fundamental groups of tensor product II$_1$ factors (English)
Yusuke Isono (RIMS, Kyoto Univ.)
On fundamental groups of tensor product II$_1$ factors (English)
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Shuta Nakajima (Research Institute for Mathematical Sciences, Kyoto University)
The cardinality of infinite geodesics originating from zero in First Passage Percolation (JAPANESE)
Shuta Nakajima (Research Institute for Mathematical Sciences, Kyoto University)
The cardinality of infinite geodesics originating from zero in First Passage Percolation (JAPANESE)
2017/05/26
Colloquium
15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Shigeki Aida (Graduate School of Mathematical Sciences, The University of Tokyo)
ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)
Shigeki Aida (Graduate School of Mathematical Sciences, The University of Tokyo)
ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)
2017/05/23
Tuesday Seminar on Topology
17:00-18:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Richard Hain (Duke University)
Johnson homomorphisms, stable and unstable (ENGLISH)
Richard Hain (Duke University)
Johnson homomorphisms, stable and unstable (ENGLISH)
[ Abstract ]
In this talk I will recall how motivic structures (Hodge and/or Galois) on the relative completions of mapping class groups yield non-trivial information about Johnson homomorphisms. I will explain how these motivic structures can be pasted, and why I believe that the genus 1 case is of fundamental importance in studying the higher genus (stable) case.
In this talk I will recall how motivic structures (Hodge and/or Galois) on the relative completions of mapping class groups yield non-trivial information about Johnson homomorphisms. I will explain how these motivic structures can be pasted, and why I believe that the genus 1 case is of fundamental importance in studying the higher genus (stable) case.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Naoki Koseki (The University of Tokyo)
Perverse coherent sheaves on blow-ups at codimension two loci (English)
Naoki Koseki (The University of Tokyo)
Perverse coherent sheaves on blow-ups at codimension two loci (English)
[ Abstract ]
I would like to talk about my recent work in progress.
Let us consider the blow-up X of Y along a subvariety C.
Then the following natural question arises:
What is the relation between moduli space of sheaves on Y
and that of X?
H.Nakajima and K.Yoshioka answered the above question
in the case when Y is a surface and C is a point. They
showed that the moduli spaces are connected by a sequence
of flip-like diagrams. The key ingredient of the proof is
to use perverse coherent sheaves in the sense of T.Bridgeland
and M.Van den Bergh.
In this talk, I will explain how to generalize their theorem
to the case when Y is a smooth projective variety of arbitrary
dimension and C is its codimension two subvariety.
I would like to talk about my recent work in progress.
Let us consider the blow-up X of Y along a subvariety C.
Then the following natural question arises:
What is the relation between moduli space of sheaves on Y
and that of X?
H.Nakajima and K.Yoshioka answered the above question
in the case when Y is a surface and C is a point. They
showed that the moduli spaces are connected by a sequence
of flip-like diagrams. The key ingredient of the proof is
to use perverse coherent sheaves in the sense of T.Bridgeland
and M.Van den Bergh.
In this talk, I will explain how to generalize their theorem
to the case when Y is a smooth projective variety of arbitrary
dimension and C is its codimension two subvariety.
Lectures
17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Frédéric Jouhet (Université Claude Bernard Lyon 1 / Institut Camille Jordan)
Enumeration of fully commutative elements in classical Coxeter groups (English)
http://math.univ-lyon1.fr/homes-www/jouhet/
Frédéric Jouhet (Université Claude Bernard Lyon 1 / Institut Camille Jordan)
Enumeration of fully commutative elements in classical Coxeter groups (English)
[ Abstract ]
An element of a Coxeter group W is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. They index naturally a basis of the (generalized) Temperley-Lieb algebra associated with W. In this talk, focusing on the (affine) type A, I will describe how to
enumerate these elements according to their Coxeter length, in all classical finite and affine Coxeter groups. The methods, which generalize previous work of Stembridge,
involve many combinatorial objects, such as heaps, walks, or parallelogram
polyominoes. This talk is based on joint works with R. Biagioli, M. Bousquet-Mélou and
P. Nadeau.
[ Reference URL ]An element of a Coxeter group W is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. They index naturally a basis of the (generalized) Temperley-Lieb algebra associated with W. In this talk, focusing on the (affine) type A, I will describe how to
enumerate these elements according to their Coxeter length, in all classical finite and affine Coxeter groups. The methods, which generalize previous work of Stembridge,
involve many combinatorial objects, such as heaps, walks, or parallelogram
polyominoes. This talk is based on joint works with R. Biagioli, M. Bousquet-Mélou and
P. Nadeau.
http://math.univ-lyon1.fr/homes-www/jouhet/
2017/05/22
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (Kyoto University)
Complex K3 surfaces containing Levi-flat hypersurfaces
Takayuki Koike (Kyoto University)
Complex K3 surfaces containing Levi-flat hypersurfaces
[ Abstract ]
We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective planes at general nine points.
We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective planes at general nine points.
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Toshihiko Masuda (Kyushu Univ.)
(English)
Toshihiko Masuda (Kyushu Univ.)
(English)
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Tawara (National Institute of Technology, Nagaoka College)
Compactness of Markov and Shcroedinger semigroups (JAPANESE)
Yoshihiro Tawara (National Institute of Technology, Nagaoka College)
Compactness of Markov and Shcroedinger semigroups (JAPANESE)
2017/05/18
Seminar on Probability and Statistics
15:00-16:10 Room #117 (Graduate School of Math. Sci. Bldg.)
Alexander A. Novikov (University of Technology Sydney)
On a representation of fractional Brownian motion and the limit distributions of statistics arising in cusp statistical models
Alexander A. Novikov (University of Technology Sydney)
On a representation of fractional Brownian motion and the limit distributions of statistics arising in cusp statistical models
[ Abstract ]
We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math. October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise" with irregular cusp-type signals. Using a new representation of fractional Brownian motion (fBm) in terms of cusp functions we show that as the noise intensity tends to zero, the limit distributions are expressed in terms of fBm for the full range of asymmetric cusp-type signals correspondingly with the Hurst parameter H, 0＜H＜1. Simulation results for the densities and variances of the limit distributions of Bayesian and maximum likelihood estimators are also provided.
We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math. October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise" with irregular cusp-type signals. Using a new representation of fractional Brownian motion (fBm) in terms of cusp functions we show that as the noise intensity tends to zero, the limit distributions are expressed in terms of fBm for the full range of asymmetric cusp-type signals correspondingly with the Hurst parameter H, 0＜H＜1. Simulation results for the densities and variances of the limit distributions of Bayesian and maximum likelihood estimators are also provided.
2017/05/17
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Olivier Fouquet (Université Paris-Sud)
The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in Hecke algebras (ENGLISH)
Olivier Fouquet (Université Paris-Sud)
The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in Hecke algebras (ENGLISH)
[ Abstract ]
The Equivariant Tamagawa Number Conjecture (ETNC) of Kato is an awe-inspiring web of conjectures predicting the special values of L-functions of motives as well as their behaviors under the action of algebras acting on motives. In this talk, I will explain the statement of the ETNC with coefficients in Hecke algebras for motives attached to modular forms, show some consequences in Iwasawa theory and outline a proof (under mild hypotheses on the residual representation) using a combination of the methods of Euler and Taylor-Wiles systems.
The Equivariant Tamagawa Number Conjecture (ETNC) of Kato is an awe-inspiring web of conjectures predicting the special values of L-functions of motives as well as their behaviors under the action of algebras acting on motives. In this talk, I will explain the statement of the ETNC with coefficients in Hecke algebras for motives attached to modular forms, show some consequences in Iwasawa theory and outline a proof (under mild hypotheses on the residual representation) using a combination of the methods of Euler and Taylor-Wiles systems.
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