## Seminar information archive

Seminar information archive ～02/19｜Today's seminar 02/20 | Future seminars 02/21～

#### thesis presentations

15:45-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

17:15-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

### 2019/01/30

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

### 2019/01/29

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Logarithmic good reduction and the index (TBA)

**Kentaro Mitsui**(Kobe)Logarithmic good reduction and the index (TBA)

[ Abstract ]

A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.

A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

The regularity of area minimizing currents modulo $p$ (English)

**Salvatore Stuvard**(The University of Texas at Austin)The regularity of area minimizing currents modulo $p$ (English)

[ Abstract ]

The theory of integer rectifiable currents was introduced by Federer and Fleming in the early 1960s in order to provide a class of generalized surfaces where the classical Plateau problem could be solved by direct methods. Since then, a number of alternative spaces of surfaces have been developed in geometric measure theory, as required for theory and applications. In particular, Fleming introduced currents modulo $2$ to treat non-orientable surfaces, and currents modulo $p$ (where $p \geq 2$ is an integer) to study more general surfaces occurring as soap films.

It is easy to see that, in general, area minimizing currents modulo $p$ need not be smooth surfaces. In this talk, I will sketch the proof of the following result, which achieves the best possible estimate for the Hausdorff dimension of the singular set of an area minimizing current modulo $p$ in the most general hypotheses, thus answering a question of White from the 1980s: if $T$ is an area minimizing current modulo $p$ of dimension $m$ in $R^{m+n}$, then $T$ is smooth at all its interior points, except those belonging to a singular set of Hausdorff dimension at most $m-1$.

The theory of integer rectifiable currents was introduced by Federer and Fleming in the early 1960s in order to provide a class of generalized surfaces where the classical Plateau problem could be solved by direct methods. Since then, a number of alternative spaces of surfaces have been developed in geometric measure theory, as required for theory and applications. In particular, Fleming introduced currents modulo $2$ to treat non-orientable surfaces, and currents modulo $p$ (where $p \geq 2$ is an integer) to study more general surfaces occurring as soap films.

It is easy to see that, in general, area minimizing currents modulo $p$ need not be smooth surfaces. In this talk, I will sketch the proof of the following result, which achieves the best possible estimate for the Hausdorff dimension of the singular set of an area minimizing current modulo $p$ in the most general hypotheses, thus answering a question of White from the 1980s: if $T$ is an area minimizing current modulo $p$ of dimension $m$ in $R^{m+n}$, then $T$ is smooth at all its interior points, except those belonging to a singular set of Hausdorff dimension at most $m-1$.

### 2019/01/28

#### Tokyo Probability Seminar

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Yosuke Kawamoto**(FUKUOKA DENTAL COLLEGE)(JAPANESE)

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Minimizing CM degree and slope stability of projective varieties (JAPANESE)

**Kentaro Ohno**(University of Tokyo)Minimizing CM degree and slope stability of projective varieties (JAPANESE)

[ Abstract ]

Chow-Mumford (CM) line bundle is considered to play an important role in moduli problem for K-stable Fano varieties. In this talk, we consider a minimization problem of the degree of the CM line bundle among all possible fillings of a polarized family over a punctured curve. We show that such minimization implies the slope semistability of the fiber if the central fiber is smooth.

Chow-Mumford (CM) line bundle is considered to play an important role in moduli problem for K-stable Fano varieties. In this talk, we consider a minimization problem of the degree of the CM line bundle among all possible fillings of a polarized family over a punctured curve. We show that such minimization implies the slope semistability of the fiber if the central fiber is smooth.

### 2019/01/22

#### Tuesday Seminar of Analysis

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Construction of solutions to Schrodinger equations with sub-quadratic potential via wave packet transform (Japanese)

**KATO Keiichi**(Tokyo University of Science)Construction of solutions to Schrodinger equations with sub-quadratic potential via wave packet transform (Japanese)

[ Abstract ]

In this talk, we consider linear Schrodinger equations with sub-quadratic potentials, which can be transformed by the wave packet transform with time dependent wave packet to a PDE of first order with inhomogeneous terms including unknown function and second derivatives of the potential. If the second derivatives of the potentials are bounded, the homogenous term of the first oder equation gives a construction of solutions to Schrodinger equations with sub-quadratic potentials by the similar way as in D. Fujiwara's work for Feynman path integral. We will show numerical computations by using our construction, if we have enough time.

In this talk, we consider linear Schrodinger equations with sub-quadratic potentials, which can be transformed by the wave packet transform with time dependent wave packet to a PDE of first order with inhomogeneous terms including unknown function and second derivatives of the potential. If the second derivatives of the potentials are bounded, the homogenous term of the first oder equation gives a construction of solutions to Schrodinger equations with sub-quadratic potentials by the similar way as in D. Fujiwara's work for Feynman path integral. We will show numerical computations by using our construction, if we have enough time.

### 2019/01/21

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

POLAR TRANSFORM AND LOCAL POSITIVITY FOR CURVES

(ENGLISH)

**Nicholas James McCleerey**(Northwestern University)POLAR TRANSFORM AND LOCAL POSITIVITY FOR CURVES

(ENGLISH)

[ Abstract ]

Using the duality of positive cones, we show that applying the polar transform from convexanalysis to local positivity invariants for divisors gives interesting and new local positivity invariantsfor curves. These new invariants have nice properties similar to those for divisors. In particular, thisenables us to give a characterization of the divisorial components of the non-K¨ahler locus of a big class. This is joint worth with Jian Xiao.

Using the duality of positive cones, we show that applying the polar transform from convexanalysis to local positivity invariants for divisors gives interesting and new local positivity invariantsfor curves. These new invariants have nice properties similar to those for divisors. In particular, thisenables us to give a characterization of the divisorial components of the non-K¨ahler locus of a big class. This is joint worth with Jian Xiao.

### 2019/01/16

#### Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)

p-adic Gelfand-Kapranov-Zelevinsky systems (ENGLISH)

**Lei Fu**(Yau Mathematical Sciences Center, Tsinghua University)p-adic Gelfand-Kapranov-Zelevinsky systems (ENGLISH)

[ Abstract ]

Using Dwork's trace formula, we express the exponential sum associated to a Laurent polynomial as the trace of a chain map on a twisted de Rham complex for the torus over the p-adic field. Treating the coefficients of the polynomial as parameters, we obtain the p-adic Gelfand-Kapranov-Zelevinsky (GKZ) system, which is a complex of D^\dagger-modules with Frobenius structure.

Using Dwork's trace formula, we express the exponential sum associated to a Laurent polynomial as the trace of a chain map on a twisted de Rham complex for the torus over the p-adic field. Treating the coefficients of the polynomial as parameters, we obtain the p-adic Gelfand-Kapranov-Zelevinsky (GKZ) system, which is a complex of D^\dagger-modules with Frobenius structure.

### 2019/01/15

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Generalized Dehn twists on surfaces and homology cylinders (JAPANESE)

**Yusuke Kuno**(Tsuda University)Generalized Dehn twists on surfaces and homology cylinders (JAPANESE)

[ Abstract ]

This is a joint work with Gwénaël Massuyeau (University of Burgundy). Lickorish's trick describes Dehn twists along simple closed curves on an oriented surface in terms of surgery of 3-manifolds. We discuss one possible generalization of this description to the situation where the curve under consideration may have self-intersections. Our result generalizes previously known computations related to the Johnson homomorphisms for the mapping class groups and for homology cylinders. In particular, we obtain an alternative and direct proof of the surjectivity of the Johnson homomorphisms for homology cylinders, which was proved by Garoufalidis-Levine and Habegger.

This is a joint work with Gwénaël Massuyeau (University of Burgundy). Lickorish's trick describes Dehn twists along simple closed curves on an oriented surface in terms of surgery of 3-manifolds. We discuss one possible generalization of this description to the situation where the curve under consideration may have self-intersections. Our result generalizes previously known computations related to the Johnson homomorphisms for the mapping class groups and for homology cylinders. In particular, we obtain an alternative and direct proof of the surjectivity of the Johnson homomorphisms for homology cylinders, which was proved by Garoufalidis-Levine and Habegger.

### 2019/01/09

#### Number Theory Seminar

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Formal groups and p-adic dynamical systems (ENGLISH)

**Laurent Berger**(ENS de Lyon)Formal groups and p-adic dynamical systems (ENGLISH)

[ Abstract ]

A formal group gives rise to a p-adic dynamical system. I will discuss some results about formal groups that can be proved using this point of view. I will also discuss the theory of p-adic dynamical systems and some open questions.

A formal group gives rise to a p-adic dynamical system. I will discuss some results about formal groups that can be proved using this point of view. I will also discuss the theory of p-adic dynamical systems and some open questions.

### 2019/01/08

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On property (T) for $\mathrm{Aut}(F_n)$ and $\mathrm{SL}_n(\mathbb{Z})$ (ENGLISH)

**Marek Kaluba**(Adam Mickiewicz Univeristy)On property (T) for $\mathrm{Aut}(F_n)$ and $\mathrm{SL}_n(\mathbb{Z})$ (ENGLISH)

[ Abstract ]

We prove that $\mathrm{Aut}(F_n)$ has Kazhdan's property (T) for every $n \ge 6$. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for $n \ge 5$. We also provide explicit lower bounds for the Kazhdan constants of $\mathrm{SAut}(F_n)$ (with $n \ge 6$) and of $\mathrm{SL}_n(\mathbb{Z})$ (with $n \ge 3$) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever $n >6$.

We prove that $\mathrm{Aut}(F_n)$ has Kazhdan's property (T) for every $n \ge 6$. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for $n \ge 5$. We also provide explicit lower bounds for the Kazhdan constants of $\mathrm{SAut}(F_n)$ (with $n \ge 6$) and of $\mathrm{SL}_n(\mathbb{Z})$ (with $n \ge 3$) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever $n >6$.

### 2018/12/25

#### Tuesday Seminar of Analysis

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Modified scattering for nonlinear dispersive equations with critical non-polynomial nonlinearities (Japanese)

**MASAKI Satoshi**(Osaka University)Modified scattering for nonlinear dispersive equations with critical non-polynomial nonlinearities (Japanese)

[ Abstract ]

In this talk, I will introduce resent progress on modified scattering for Schrodinger equation and Klein-Gordon equation with a non-polynomial nonlinearity. We use Fourier series expansion technique to find the resonant part of the nonlinearity which produces phase correction factor.

In this talk, I will introduce resent progress on modified scattering for Schrodinger equation and Klein-Gordon equation with a non-polynomial nonlinearity. We use Fourier series expansion technique to find the resonant part of the nonlinearity which produces phase correction factor.

#### Infinite Analysis Seminar Tokyo

16:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Q-operators for generalised eight vertex models associated

to the higher spin representations of the Sklyanin algebra. (ENGLISH)

**Takashi Takebe**(National Research University Higher School of Economics (Moscow))Q-operators for generalised eight vertex models associated

to the higher spin representations of the Sklyanin algebra. (ENGLISH)

[ Abstract ]

The Q-operator was first introduced by Baxter in 1972 as a

tool to solve the eight vertex model and recently attracts

attention from the representation theoretical viewpoint. In

this talk, we show that Baxter's apparently quite ad hoc and

technical construction can be generalised to the model

associated to the higher spin representations of the

Sklyanin algebra. If everybody in the audience understands Japanese, the talk

will be in Japanese.

The Q-operator was first introduced by Baxter in 1972 as a

tool to solve the eight vertex model and recently attracts

attention from the representation theoretical viewpoint. In

this talk, we show that Baxter's apparently quite ad hoc and

technical construction can be generalised to the model

associated to the higher spin representations of the

Sklyanin algebra. If everybody in the audience understands Japanese, the talk

will be in Japanese.

### 2018/12/21

#### Algebraic Geometry Seminar

10:30-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Degenerations of p-adic volume forms (English)

**Mattias Jonsson**(Michigan)Degenerations of p-adic volume forms (English)

[ Abstract ]

Let X be an n-dimensional smooth projective variety over a non-Archimedean local field K. Also fix a regular n-form on X. This data induces a positive measure on the space of K'-rational points for any finite extension K' of K. We describe the asymptotics, as K' runs through towers of finite extensions of K, in terms of Berkovich analytic geometry. This is joint work with Johannes Nicaise.

Let X be an n-dimensional smooth projective variety over a non-Archimedean local field K. Also fix a regular n-form on X. This data induces a positive measure on the space of K'-rational points for any finite extension K' of K. We describe the asymptotics, as K' runs through towers of finite extensions of K, in terms of Berkovich analytic geometry. This is joint work with Johannes Nicaise.

### 2018/12/20

#### Tuesday Seminar on Topology

13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Johnson-type homomorphisms and the LMO functor (ENGLISH)

**Anderson Vera**(Université de Strasbourg)Johnson-type homomorphisms and the LMO functor (ENGLISH)

[ Abstract ]

One of the main objects associated to a surface S is the mapping class group MCG(S). This group plays an important role in the study of 3-manifolds. Reciprocally, the topological invariants of 3-manifolds can be used to obtain interesting representations of MCG(S).

One possible approach to the study of MCG(S) is to consider its action on the fundamental group P of the surface or on some subgroups of P. This way, we can obtain some kind of filtrations of MCG(S) and homomorphisms, called Johnson type homomorphisms, which take values in certain spaces of diagrams. These spaces of diagrams are quotients of the target space of the LMO functor. Hence it is natural to ask what is the relation between the Johnson type homomorphisms and the LMO functor. The answer is well known in the case of the Torelli group and the usual Johnson homomorphisms. In this talk we consider two other different filtrations of MCG(S) introduced by Levine and Habiro-Massuyeau. We show that the respective Johnson homomorphisms can also be deduced from the LMO functor.

One of the main objects associated to a surface S is the mapping class group MCG(S). This group plays an important role in the study of 3-manifolds. Reciprocally, the topological invariants of 3-manifolds can be used to obtain interesting representations of MCG(S).

One possible approach to the study of MCG(S) is to consider its action on the fundamental group P of the surface or on some subgroups of P. This way, we can obtain some kind of filtrations of MCG(S) and homomorphisms, called Johnson type homomorphisms, which take values in certain spaces of diagrams. These spaces of diagrams are quotients of the target space of the LMO functor. Hence it is natural to ask what is the relation between the Johnson type homomorphisms and the LMO functor. The answer is well known in the case of the Torelli group and the usual Johnson homomorphisms. In this talk we consider two other different filtrations of MCG(S) introduced by Levine and Habiro-Massuyeau. We show that the respective Johnson homomorphisms can also be deduced from the LMO functor.

### 2018/12/19

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Polynomial Time Algorithm for Computing N-th Moments of a Self-Adjoint Operator in Algebra Generated by Free Independent Semicircular Elements

**Rei Mizuta**(Univ. Tokyo)Polynomial Time Algorithm for Computing N-th Moments of a Self-Adjoint Operator in Algebra Generated by Free Independent Semicircular Elements

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Cohomology vanishing for automorphic vector bundles (ENGLISH)

**Jean-Stefan Koskivirta**(University of Tokyo)Cohomology vanishing for automorphic vector bundles (ENGLISH)

[ Abstract ]

A Shimura variety carries naturally a family of vector bundles parametrized by the characters of a maximal torus in the attached group. We want to determine which of these vector bundles are ample, and also show cohomology vanishing results. For this we use generalized Hasse invariants on the stack of G-zips of Moonen-Pink-Wedhorn-Ziegler. It is a group-theoretical counterpart of the Shimura variety and carries a similar family of vector bundles. This is joint work with Y.Brunebarbe, W.Goldring and B.Stroh.

A Shimura variety carries naturally a family of vector bundles parametrized by the characters of a maximal torus in the attached group. We want to determine which of these vector bundles are ample, and also show cohomology vanishing results. For this we use generalized Hasse invariants on the stack of G-zips of Moonen-Pink-Wedhorn-Ziegler. It is a group-theoretical counterpart of the Shimura variety and carries a similar family of vector bundles. This is joint work with Y.Brunebarbe, W.Goldring and B.Stroh.

### 2018/12/18

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Dynamics of singular vortex patches (English)

**In-Jee Jeong**(Korea Institute for Advanced Study (KIAS))Dynamics of singular vortex patches (English)

[ Abstract ]

Vortex patches are solutions to the 2D Euler equations that are given by the characteristic function of a bounded domain that moves with time. It is well-known that if initially the boundary of the domain is smooth, the boundary remains smooth for all time. On the other hand, we consider patches with corner singularities. It turns out that, depending on whether the initial patch satisfies an appropriate rotational symmetry condition or not, the corner structure may propagate for all time or lost immediately. In the rotationally symmetric case, we are able to construct patches with interesting dynamical behavior as time goes to infinity. When the symmetry is absent, we present a simple yet formal evolution equation which describes the dynamics of the boundary. It suggests that the angle cusps instantaneously for $t > 0$.

This is joint work with Tarek Elgindi.

Vortex patches are solutions to the 2D Euler equations that are given by the characteristic function of a bounded domain that moves with time. It is well-known that if initially the boundary of the domain is smooth, the boundary remains smooth for all time. On the other hand, we consider patches with corner singularities. It turns out that, depending on whether the initial patch satisfies an appropriate rotational symmetry condition or not, the corner structure may propagate for all time or lost immediately. In the rotationally symmetric case, we are able to construct patches with interesting dynamical behavior as time goes to infinity. When the symmetry is absent, we present a simple yet formal evolution equation which describes the dynamics of the boundary. It suggests that the angle cusps instantaneously for $t > 0$.

This is joint work with Tarek Elgindi.

#### Tuesday Seminar on Topology

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Discrete G-spectra and a model for the K(n)-local stable homotopy category (JAPANESE)

**Takeshi Torii**(Okayama University)Discrete G-spectra and a model for the K(n)-local stable homotopy category (JAPANESE)

[ Abstract ]

The K(n)-local stable homotopy categories are building blocks for the stable homotopy category of spectra. In this talk I will construct a model for the K(n)-local stable homotopy category, which explicitly shows the relationship with the Morava E-theory E_n and the stabilizer group G_n. We consider discrete symmetric G-spectra studied by Behrens-Davis for a profinite group G. I will show that the K(n)-local stable homotopy category is realized in the homotopy category of modules in discrete symmetric G_n-spectra over a discrete model of E_n.

The K(n)-local stable homotopy categories are building blocks for the stable homotopy category of spectra. In this talk I will construct a model for the K(n)-local stable homotopy category, which explicitly shows the relationship with the Morava E-theory E_n and the stabilizer group G_n. We consider discrete symmetric G-spectra studied by Behrens-Davis for a profinite group G. I will show that the K(n)-local stable homotopy category is realized in the homotopy category of modules in discrete symmetric G_n-spectra over a discrete model of E_n.

### 2018/12/17

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Newton polyhedra and order of contact on real hypersurfaces (JAPANESE)

**Joe Kamimoto**(Kyushu University)Newton polyhedra and order of contact on real hypersurfaces (JAPANESE)

[ Abstract ]

This talk will concern some issues on order of contact on real hypersurfaces, which was introduced by D'Angelo. To be more precise, a sufficient condition for the equality of regular type and singular type is given. This condition is written by using the Newton polyhedron of a defining function. Our result includes earlier known results concerning convex domains, pseudoconvex Reinhardt domains and pseudoconvex domains whose regular types are 4. Furthermore, under the above condition, the values of the types can be directly seen in a simple geometrical information from the Newton polyhedron.

The technique of using Newton polyhedra has many significant applications in singularity theory. In particular, this technique has been great success in the study of the Lojasiewicz exponent. Our study about the types is analogous to some works on the Lojasiewicz exponent.

This talk will concern some issues on order of contact on real hypersurfaces, which was introduced by D'Angelo. To be more precise, a sufficient condition for the equality of regular type and singular type is given. This condition is written by using the Newton polyhedron of a defining function. Our result includes earlier known results concerning convex domains, pseudoconvex Reinhardt domains and pseudoconvex domains whose regular types are 4. Furthermore, under the above condition, the values of the types can be directly seen in a simple geometrical information from the Newton polyhedron.

The technique of using Newton polyhedra has many significant applications in singularity theory. In particular, this technique has been great success in the study of the Lojasiewicz exponent. Our study about the types is analogous to some works on the Lojasiewicz exponent.

### 2018/12/14

#### Algebraic Geometry Seminar

10:30-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

On the birationality of quint-canonical systems of irregular threefolds of general type (English)

**Zhi Jiang**(Fudan)On the birationality of quint-canonical systems of irregular threefolds of general type (English)

[ Abstract ]

It is well-known that the quint-canonical map of a surface of general type is birational.

We will show that the same result holds for irregular threefolds of general type. The proof is based on

a careful study of the positivity of the pushforwards of pluricanonical bundles on abelian varieties and Severi

type inequalities. This is a joint work with J.A. Chen, J.Chen, and M.Chen.

It is well-known that the quint-canonical map of a surface of general type is birational.

We will show that the same result holds for irregular threefolds of general type. The proof is based on

a careful study of the positivity of the pushforwards of pluricanonical bundles on abelian varieties and Severi

type inequalities. This is a joint work with J.A. Chen, J.Chen, and M.Chen.

### 2018/12/12

#### Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)

A higher weight (and automorphic) generalization of the Hermite-Minkowski theorem (ENGLISH)

**Gaëtan Chenevier**(CNRS, Université Paris-Sud)A higher weight (and automorphic) generalization of the Hermite-Minkowski theorem (ENGLISH)

[ Abstract ]

I will show that for any integer N, there are only finitely many cuspidal algebraic automorphic representations of GL_m over Q whose Artin conductor is N and whose "weights" are in the interval {0,...,23} (with m varying). Via the conjectural yoga between geometric Galois representations (or motives) and algebraic automorphic forms, this statement may be viewed as a generalization of the classical Hermite-Minkowski theorem in algebraic number theory. I will also discuss variants of these results when the base field Q is replaced by an arbitrary number field.

I will show that for any integer N, there are only finitely many cuspidal algebraic automorphic representations of GL_m over Q whose Artin conductor is N and whose "weights" are in the interval {0,...,23} (with m varying). Via the conjectural yoga between geometric Galois representations (or motives) and algebraic automorphic forms, this statement may be viewed as a generalization of the classical Hermite-Minkowski theorem in algebraic number theory. I will also discuss variants of these results when the base field Q is replaced by an arbitrary number field.

### 2018/12/11

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Solutions with moving singularities for equations of porous medium type (English)

**Marek Fila**(Comenius University in Bratislava)Solutions with moving singularities for equations of porous medium type (English)

[ Abstract ]

We construct positive solutions of equations of porous medium type with a singularity which moves in time along a prescribed curve and keeps the spatial profile of singular stationary solutions. It turns out that there appears a critical exponent for the existence of such solutions. This is a joint work with Jin Takahashi and Eiji Yanagida.

We construct positive solutions of equations of porous medium type with a singularity which moves in time along a prescribed curve and keeps the spatial profile of singular stationary solutions. It turns out that there appears a critical exponent for the existence of such solutions. This is a joint work with Jin Takahashi and Eiji Yanagida.

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143 Next >