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Seminar information archive
Seminar information archive ～04/18｜Today's seminar 04/19 | Future seminars 04/20～
Tokyo-Nagoya Algebra Seminar
13:00-14:30 Online
Please see the reference URL for details on the online seminar.
Takumi Otani (Osaka Univeristy)
Full exceptional collections associated with Bridgeland stability conditions (Japanese)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Takumi Otani (Osaka Univeristy)
Full exceptional collections associated with Bridgeland stability conditions (Japanese)
[ Abstract ]
The space of Bridgeland stability conditions on a triangulated category is important in mirror symmetry and many people develop various techniques to study it. In order to study the homotopy type of the space of stability conditions, Macri studied stability conditions associated with full exceptional collections. Based on his work, Dimitrov-Katzarkov introduced the notion of a full σ-exceptional collection for a stability condition σ.
In this talk, I will explain the relationship between full exceptional collections and stability conditions and some properties. I will also talk about the existence of full σ-exceptional collections for the derived category of an acyclic quiver.
[ Reference URL ]The space of Bridgeland stability conditions on a triangulated category is important in mirror symmetry and many people develop various techniques to study it. In order to study the homotopy type of the space of stability conditions, Macri studied stability conditions associated with full exceptional collections. Based on his work, Dimitrov-Katzarkov introduced the notion of a full σ-exceptional collection for a stability condition σ.
In this talk, I will explain the relationship between full exceptional collections and stability conditions and some properties. I will also talk about the existence of full σ-exceptional collections for the derived category of an acyclic quiver.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)
Taro Yoshino (Tokyo)
On the degree of irrationality of complete intersections (Japanese )
Taro Yoshino (Tokyo)
On the degree of irrationality of complete intersections (Japanese )
[ Abstract ]
The degree of irrationality of a variety X is the minimum degree of a dominant, generically finite rational map from X to a rational variety. This invariant gives a measure of how far X is from being rational. There were some varieties whose degree of irrationality was computed. For example, in 2017, Bastianelli, De Poi, Ein, Lazarsfeld, and Ullery computed the degree of irrationality of very general hypersurfaces of general type by using the positivity of the canonical line bundle. On the other hand, in 2020, Chen and Stapleton obtained the lower bound of the degree of irrationality of very general Fano hypersurfaces by using the reduction of modulo p.
In this talk, we will show that we can obtain the lower bound of the degree of irrationality of very general Fano complete intersections. For obtaining the bound, we make a minor adjustment to Chen--Stapleton's method using the trace map of differential modules.
This talk is based on joint work with Lucas Braune.
The degree of irrationality of a variety X is the minimum degree of a dominant, generically finite rational map from X to a rational variety. This invariant gives a measure of how far X is from being rational. There were some varieties whose degree of irrationality was computed. For example, in 2017, Bastianelli, De Poi, Ein, Lazarsfeld, and Ullery computed the degree of irrationality of very general hypersurfaces of general type by using the positivity of the canonical line bundle. On the other hand, in 2020, Chen and Stapleton obtained the lower bound of the degree of irrationality of very general Fano hypersurfaces by using the reduction of modulo p.
In this talk, we will show that we can obtain the lower bound of the degree of irrationality of very general Fano complete intersections. For obtaining the bound, we make a minor adjustment to Chen--Stapleton's method using the trace map of differential modules.
This talk is based on joint work with Lucas Braune.
2023/04/27
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuaki Okamoto (NTT)
The basics of cryptography II (Japanese)
Tatsuaki Okamoto (NTT)
The basics of cryptography II (Japanese)
[ Abstract ]
Explanation of the basics of cryptography
Explanation of the basics of cryptography
2023/04/26
Number Theory Seminar
18:00-19:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Live transmission from IHES, Warning: Start time is one hour later than usual.
Dustin Clausen (Institut des Hautes Études Scientifiques)
A Conjectural Reciprocity Law for Realizations of Motives
https://indico.math.cnrs.fr/event/9634/
Live transmission from IHES, Warning: Start time is one hour later than usual.
Dustin Clausen (Institut des Hautes Études Scientifiques)
A Conjectural Reciprocity Law for Realizations of Motives
[ Abstract ]
A motive over a scheme S is a bit of linear algebra which is supposed to "universally" capture the cohomology of smooth proper S-schemes. Motives can be studied via various "realizations", which are objects of more concrete linear algebraic categories attached to S. It is known that over certain S, these different realizations are related to one another via comparison isomorphisms, as in Hodge theory. In this talk, I will try to explain that for completely general S, there is a much more subtle kind of relationship between these realizations, which takes a similar form to classical reciprocity laws in number theory.
[ Reference URL ]A motive over a scheme S is a bit of linear algebra which is supposed to "universally" capture the cohomology of smooth proper S-schemes. Motives can be studied via various "realizations", which are objects of more concrete linear algebraic categories attached to S. It is known that over certain S, these different realizations are related to one another via comparison isomorphisms, as in Hodge theory. In this talk, I will try to explain that for completely general S, there is a much more subtle kind of relationship between these realizations, which takes a similar form to classical reciprocity laws in number theory.
https://indico.math.cnrs.fr/event/9634/
2023/04/25
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Hiraku Nozawa (Ritsumeikan University)
Harmonic measures and rigidity of surface group actions on the circle (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Hiraku Nozawa (Ritsumeikan University)
Harmonic measures and rigidity of surface group actions on the circle (JAPANESE)
[ Abstract ]
We study rigidity properties of surface group actions on the circle via harmonic measures on the suspension bundles, which are measures invariant under the heat diffusion along leaves. We will explain a curvature estimate and a Gauss-Bonnet formula for an S^1-connection obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of semiconjugacy rigidity theorems of Matsumoto and Burger-Iozzi-Wienhard for actions with maximal Euler number. This is joint work with Masanori Adachi and Yoshifumi Matsuda.
[ Reference URL ]We study rigidity properties of surface group actions on the circle via harmonic measures on the suspension bundles, which are measures invariant under the heat diffusion along leaves. We will explain a curvature estimate and a Gauss-Bonnet formula for an S^1-connection obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of semiconjugacy rigidity theorems of Matsumoto and Burger-Iozzi-Wienhard for actions with maximal Euler number. This is joint work with Masanori Adachi and Yoshifumi Matsuda.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Taihei Oki (The University of Tokyo)
Combinatorial preprocessing methods for differential-algebraic equations (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Taihei Oki (The University of Tokyo)
Combinatorial preprocessing methods for differential-algebraic equations (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2023/04/24
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
On site+Zoom
Takeo Ohsawa (Nogoya Universiry)
Guan's theorems on optimal strong openness and concavity of minimal $L^2$ integrals (日本語)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
On site+Zoom
Takeo Ohsawa (Nogoya Universiry)
Guan's theorems on optimal strong openness and concavity of minimal $L^2$ integrals (日本語)
[ Abstract ]
Motivated by a question of approximating plurisubharmonic (=psh) functions by those with tame singularities, Demailly and Kollar asked several basic questions on the singularities of psh functions. Guan solved two of them effectively in a paper published in 2019. One of their corollaries says the following.
THEOREM. Let $\Omega$ be a pseudoconvex domain in $\mathbb{C}^n$ and let $\varphi$ be a negative psh function on $\Omega$ such that $\int_\Omega{e^{-\varphi}}<\infty$. Then, $e^{-p\varphi}\in L^1_{\text{loc}}$ around $x$ for any $x\in\Omega$ and $p>1$ satisfying the inequality $$
\frac{p}{p-1}>\frac{\int_\Omega{e^{-\varphi}}}{K_\Omega(x)},
$$ where $K_\Omega$ denotes the diagonalized Bergman kernel of $\Omega$.
This remarkable result is a consequence of a basic property of the minimal $L^2$ integrals (=MLI). The main purpose of the talk is to give an outline of the proof of Theorem by explaining the relation between several notions including the MLI which measure the singularities of psh functions. It will also be mentioned that the proof of Theorem is essentially based on the optimal Ohsawa-Takegoshi type extension theorem, which leads to a concavity property of MLI. Recent papers by Guan and his students will be reviewed, too.
[ Reference URL ]Motivated by a question of approximating plurisubharmonic (=psh) functions by those with tame singularities, Demailly and Kollar asked several basic questions on the singularities of psh functions. Guan solved two of them effectively in a paper published in 2019. One of their corollaries says the following.
THEOREM. Let $\Omega$ be a pseudoconvex domain in $\mathbb{C}^n$ and let $\varphi$ be a negative psh function on $\Omega$ such that $\int_\Omega{e^{-\varphi}}<\infty$. Then, $e^{-p\varphi}\in L^1_{\text{loc}}$ around $x$ for any $x\in\Omega$ and $p>1$ satisfying the inequality $$
\frac{p}{p-1}>\frac{\int_\Omega{e^{-\varphi}}}{K_\Omega(x)},
$$ where $K_\Omega$ denotes the diagonalized Bergman kernel of $\Omega$.
This remarkable result is a consequence of a basic property of the minimal $L^2$ integrals (=MLI). The main purpose of the talk is to give an outline of the proof of Theorem by explaining the relation between several notions including the MLI which measure the singularities of psh functions. It will also be mentioned that the proof of Theorem is essentially based on the optimal Ohsawa-Takegoshi type extension theorem, which leads to a concavity property of MLI. Recent papers by Guan and his students will be reviewed, too.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Tokyo Probability Seminar
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Charles Bordenave (Institut de Mathématiques de Marseille)
Mobility edge, the Poisson Infinite weighted tree of Aldous and Lévy Matrices (English)
Charles Bordenave (Institut de Mathématiques de Marseille)
Mobility edge, the Poisson Infinite weighted tree of Aldous and Lévy Matrices (English)
[ Abstract ]
Anderson's 1958 paper on wave scattering in disordered media is still of central importance in contemporary mathematical physics. In this talk, we will present recent progress in understanding the phenomena of localization / delocalization of eigenwaves for some random operators. These operators are built on random trees introduced by Aldous and these are the scaling limits of heavy-tailed random matrices, the Lévy matrices. The focus will be put on the existence of a mobility edge, that is to say of かn abrupt transition between localization and delocalization of eigenwaves. It is a work in collaboration with Amol Aggarwal (Columbia) and Patrick Lopatto (NYU).
Anderson's 1958 paper on wave scattering in disordered media is still of central importance in contemporary mathematical physics. In this talk, we will present recent progress in understanding the phenomena of localization / delocalization of eigenwaves for some random operators. These operators are built on random trees introduced by Aldous and these are the scaling limits of heavy-tailed random matrices, the Lévy matrices. The focus will be put on the existence of a mobility edge, that is to say of かn abrupt transition between localization and delocalization of eigenwaves. It is a work in collaboration with Amol Aggarwal (Columbia) and Patrick Lopatto (NYU).
Infinite Analysis Seminar Tokyo
16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Takahiko Nobukawa (Kobe University )
Euler type integral formulas and hypergeometric solutions for
variants of the $q$ hypergeometric equations.
(Japanese)
Takahiko Nobukawa (Kobe University )
Euler type integral formulas and hypergeometric solutions for
variants of the $q$ hypergeometric equations.
(Japanese)
[ Abstract ]
We know that Papperitz's differential equation is essentially obtained from
Gauss' hypergeometric equation by applying a Moebius transformation,
implying that we have Euler type integral formulas or hypergeometric solutions.
The variants of the $q$ hypergeometric equations, introduced by
Hatano-Matsunawa-Sato-Takemura (Funkcial. Ekvac.,2022), are second order
$q$-difference systems which can be regarded as $q$ analoges of Papperitz's equation.
This motivates us for deriving Euler type integral formulas and hypergeometric solutions
for the pertinent $q$-difference systems. If time admits, I explain
the relation with $q$-analogues of Kummer's 24 solutions,
or the variants of multivariate $q$-hypergeometric functions.
This talk is based on the collaboration with Taikei Fujii.
We know that Papperitz's differential equation is essentially obtained from
Gauss' hypergeometric equation by applying a Moebius transformation,
implying that we have Euler type integral formulas or hypergeometric solutions.
The variants of the $q$ hypergeometric equations, introduced by
Hatano-Matsunawa-Sato-Takemura (Funkcial. Ekvac.,2022), are second order
$q$-difference systems which can be regarded as $q$ analoges of Papperitz's equation.
This motivates us for deriving Euler type integral formulas and hypergeometric solutions
for the pertinent $q$-difference systems. If time admits, I explain
the relation with $q$-analogues of Kummer's 24 solutions,
or the variants of multivariate $q$-hypergeometric functions.
This talk is based on the collaboration with Taikei Fujii.
2023/04/21
Tokyo-Nagoya Algebra Seminar
13:00-14:30 Online
Please see the reference URL for details on the online seminar.
Kota Murakami (University of Tokyo)
Categorifications of deformed Cartan matrices (Japanese)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Kota Murakami (University of Tokyo)
Categorifications of deformed Cartan matrices (Japanese)
[ Abstract ]
In a series of works of Gei\ss-Leclerc-Schr\″oer, they introduced a version of preprojective algebra associated with a symmetrizable generalized Cartan matrix and its symmetrizer. For finite type, it can be regarded as an un-graded analogue of Jacobian algebra of certain quiver with potential appeared in the theory of (monoidal) categorification of cluster algebras.
In this talk, we will present an interpretation of graded structures of the preprojective algebra of general type, in terms of a multi-parameter deformation of generalized Cartan matrix and relevant combinatorics motivated from several contexts in the theory of quantum loop algebras or quiver $\mathcal{W}$-algebras. From the vantage point of the representation theory of preprojective algebra, we will prove several purely combinatorial properties of these concepts. This talk is based on a joint work with Ryo Fujita (RIMS).
[ Reference URL ]In a series of works of Gei\ss-Leclerc-Schr\″oer, they introduced a version of preprojective algebra associated with a symmetrizable generalized Cartan matrix and its symmetrizer. For finite type, it can be regarded as an un-graded analogue of Jacobian algebra of certain quiver with potential appeared in the theory of (monoidal) categorification of cluster algebras.
In this talk, we will present an interpretation of graded structures of the preprojective algebra of general type, in terms of a multi-parameter deformation of generalized Cartan matrix and relevant combinatorics motivated from several contexts in the theory of quantum loop algebras or quiver $\mathcal{W}$-algebras. From the vantage point of the representation theory of preprojective algebra, we will prove several purely combinatorial properties of these concepts. This talk is based on a joint work with Ryo Fujita (RIMS).
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Algebraic Geometry Seminar
14:00-15:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Tatsuro Kawakami (Kyoto University)
Endomorphisms of varieties and Bott vanishing (Japanese)
Tatsuro Kawakami (Kyoto University)
Endomorphisms of varieties and Bott vanishing (Japanese)
[ Abstract ]
In this talk, we show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. This talk is based on joint work with Burt Totaro.
In this talk, we show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. This talk is based on joint work with Burt Totaro.
Algebraic Geometry Seminar
12:45-13:45 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)
Sung Rak Choi (Yonsei University )
ACC of plc thresholds (English)
Sung Rak Choi (Yonsei University )
ACC of plc thresholds (English)
[ Abstract ]
The notion of potential pairs was developed as a means to bound the singularities while running the anti-MMP. They behave similarly with the usual klt, lc pairs.
We introduce potential log canonical threshold and prove that the set of these thresholds also satisfies the ascending chain condition (ACC). We also study the relation with the complements. This is a joint work with Sungwook Jang.
The notion of potential pairs was developed as a means to bound the singularities while running the anti-MMP. They behave similarly with the usual klt, lc pairs.
We introduce potential log canonical threshold and prove that the set of these thresholds also satisfies the ascending chain condition (ACC). We also study the relation with the complements. This is a joint work with Sungwook Jang.
2023/04/20
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuaki Okamoto (NTT)
The basics of cryptography (Japanese)
Tatsuaki Okamoto (NTT)
The basics of cryptography (Japanese)
[ Abstract ]
Explanation of the basics of cryptography
Explanation of the basics of cryptography
2023/04/19
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Nicola Mazzari (University of Padua)
The conjugate uniformization in the semistable case (English)
https://sites.google.com/site/nclmzzr/
Nicola Mazzari (University of Padua)
The conjugate uniformization in the semistable case (English)
[ Abstract ]
We will review some recent results by Iovita-Morrow-Zaharescu about p-adic uniformization of abelian varieties with good reduction. Most of it relies on the theory developed by Fontaine especially about almost Cp-representations. These results were recently generalised by Howe-Morrow-Wear, via p-divisible groups.
We will explain how to treat the semistable case with focus on some really basic example, like the Tate elliptic curve.
[ Reference URL ]We will review some recent results by Iovita-Morrow-Zaharescu about p-adic uniformization of abelian varieties with good reduction. Most of it relies on the theory developed by Fontaine especially about almost Cp-representations. These results were recently generalised by Howe-Morrow-Wear, via p-divisible groups.
We will explain how to treat the semistable case with focus on some really basic example, like the Tate elliptic curve.
https://sites.google.com/site/nclmzzr/
2023/04/18
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Naoki Genra (Univ. Tokyo)
Representation theory of subregular W-algebras and principal W-superalgebras (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Naoki Genra (Univ. Tokyo)
Representation theory of subregular W-algebras and principal W-superalgebras (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Naoki Genra (Univ. Tokyo)
Representation theory of subregular W-algebras and principal W-superalgebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Naoki Genra (Univ. Tokyo)
Representation theory of subregular W-algebras and principal W-superalgebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Shuhei Maruyama (Chuo University)
A crossed homomorphism on a big mapping class group (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Shuhei Maruyama (Chuo University)
A crossed homomorphism on a big mapping class group (JAPANESE)
[ Abstract ]
Big mapping class groups are mapping class groups of surfaces of infinite type. Calegari and Chen determined the second (co)homology group of the mapping class group of the sphere minus a Cantor set. They also raised related questions: one of the questions asks an explicit form of certain crossed homomorphisms on the big mapping class group. In this talk, we provide a construction of crossed homomorphisms via group actions on the circle, which answers the question of Calegari and Chen.
[ Reference URL ]Big mapping class groups are mapping class groups of surfaces of infinite type. Calegari and Chen determined the second (co)homology group of the mapping class group of the sphere minus a Cantor set. They also raised related questions: one of the questions asks an explicit form of certain crossed homomorphisms on the big mapping class group. In this talk, we provide a construction of crossed homomorphisms via group actions on the circle, which answers the question of Calegari and Chen.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023/04/17
Tokyo Probability Seminar
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
清水良輔 (早稲田大学)
Construction of Sobolev spaces and energies on the Sierpinski carpet (Japanese)
清水良輔 (早稲田大学)
Construction of Sobolev spaces and energies on the Sierpinski carpet (Japanese)
2023/04/13
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuaki Okamoto (NTT)
Certification and signature
------Foundation of cryptography (Japanese)
Tatsuaki Okamoto (NTT)
Certification and signature
------Foundation of cryptography (Japanese)
[ Abstract ]
Explanation on certification and signature.
Explanation on certification and signature.
2023/04/11
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kazuo Habiro (The Univesity of Tokyo)
On the stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kazuo Habiro (The Univesity of Tokyo)
On the stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)
[ Abstract ]
By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.
[ Reference URL ]By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023/04/06
Applied Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Van Tien Nguyen (National Taiwan University)
Blowup solutions to the Keller-Segel system (English)
https://forms.gle/7ogZKyh1oXKkPbN56
Van Tien Nguyen (National Taiwan University)
Blowup solutions to the Keller-Segel system (English)
[ Abstract ]
I will present constructive examples of finite-time blowup solutions to the Keller-Segel system in $\mathbb{R}^d$. For $d = 2$ ($L^1$-critical), there are finite time blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized according to a discrete spectrum of a linearized operator around the rescaled stationary solution in the self-similar setting. There is a stable blowup mechanism which is expected to be generic among others. For $d \geq 3$ ($L^1$-supercritical), we construct finite time blowup solutions that are completely unrelated to the self-similar scale, in particular, they are of Type II with finite mass. Interestingly, the radial blowup profile is linked to the traveling-wave of the 1D viscous Burgers equation. Our constructed solution actually has the form of collapsing-ring which consists of an imploding, smoothed-out shock wave moving towards the origin to form a Dirac mass at the singularity. I will also discuss other blowup patterns that possibly occur in the cases $d = 2,3,4$.
[ Reference URL ]I will present constructive examples of finite-time blowup solutions to the Keller-Segel system in $\mathbb{R}^d$. For $d = 2$ ($L^1$-critical), there are finite time blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized according to a discrete spectrum of a linearized operator around the rescaled stationary solution in the self-similar setting. There is a stable blowup mechanism which is expected to be generic among others. For $d \geq 3$ ($L^1$-supercritical), we construct finite time blowup solutions that are completely unrelated to the self-similar scale, in particular, they are of Type II with finite mass. Interestingly, the radial blowup profile is linked to the traveling-wave of the 1D viscous Burgers equation. Our constructed solution actually has the form of collapsing-ring which consists of an imploding, smoothed-out shock wave moving towards the origin to form a Dirac mass at the singularity. I will also discuss other blowup patterns that possibly occur in the cases $d = 2,3,4$.
https://forms.gle/7ogZKyh1oXKkPbN56
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuaki Okamoto (NTT)
The role of cryptography (Japanese)
Tatsuaki Okamoto (NTT)
The role of cryptography (Japanese)
[ Abstract ]
Explanation of the theory of cryptography
Explanation of the theory of cryptography
2023/03/28
Algebraic Geometry Seminar
10:00-11:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Paolo Cascini (Imperial College London)
On the canonical bundle formula in positive characteristic (English)
Paolo Cascini (Imperial College London)
On the canonical bundle formula in positive characteristic (English)
[ Abstract ]
In a previous work in collaboration with F. Ambro, V. Shokurov and C. Spicer, we show that algebraically integrable foliations can be used to study the canonical bundle formula for fibrations which are not necessarily lc trivial.
I will discuss a work in progress by M. Benozzo on a generalisation of these results in positive characteristic.
In a previous work in collaboration with F. Ambro, V. Shokurov and C. Spicer, we show that algebraically integrable foliations can be used to study the canonical bundle formula for fibrations which are not necessarily lc trivial.
I will discuss a work in progress by M. Benozzo on a generalisation of these results in positive characteristic.
2023/03/24
Mathematical Biology Seminar
10:00-11:00 Online
Toshiyuki Namba (Osaka Metropolitan University)
Unexpected coexistence and extinction in an intraguild predation system (Japanese)
Toshiyuki Namba (Osaka Metropolitan University)
Unexpected coexistence and extinction in an intraguild predation system (Japanese)
2023/03/14
Tuesday Seminar of Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Piermarco Cannarsa (University of Rome "Tor Vergata")
Parameter reconstruction for degenerate parabolic equations (English)
https://forms.gle/nejpQS824vFKRbMQ6
Piermarco Cannarsa (University of Rome "Tor Vergata")
Parameter reconstruction for degenerate parabolic equations (English)
[ Abstract ]
First, we study degenerate parabolic equations arising in climate dynamics, providing uniqueness and stability estimates for the determination of the insolation function. Then, we address several aspects of the reconstruction of the degenerate diffusion coefficient. Finally, we discuss systems of two equations including a vertical component into the model.
[ Reference URL ]First, we study degenerate parabolic equations arising in climate dynamics, providing uniqueness and stability estimates for the determination of the insolation function. Then, we address several aspects of the reconstruction of the degenerate diffusion coefficient. Finally, we discuss systems of two equations including a vertical component into the model.
https://forms.gle/nejpQS824vFKRbMQ6
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