過去の記録 ~02/21本日 02/22 | 今後の予定 02/23~



10:30-12:00   数理科学研究科棟(駒場) 126号室
糟谷 久矢 氏 (東京工業大学)
Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds (Japanese)
[ 講演概要 ]
By the result of Deligne, Griffiths, Morgan and Sullivan, the Malcev completion of the fundamental group of a compact Kahler manifold is quadratically presented. This fact gives good advances in "Kahler group problem" (Which groups can be the fundamental groups of compact Kahler manifolds?) In this talk, we consider the fundamental groups of compact Sasakian manifolds. We show that the Malcev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n >= 2 admits a quadratic presentation by using Morgan's bigradings of Sullivan's minimal models of mixed-Hodge diagrams.


16:50-18:20   数理科学研究科棟(駒場) 128号室
横山 聡 氏 (東京大学大学院数理科学研究科)
On a stochastic Rayleigh-Plesset equation and a certain stochastic Navier-Stokes equation



10:00-11:30   数理科学研究科棟(駒場) 126号室
四之宮佳彦 氏 (静岡大学)
Veech groups of Veech surfaces and periodic points (日本語)
[ 講演概要 ]


16:20-17:30   数理科学研究科棟(駒場) 056号室
足立高徳 氏 (立命館大学)
A Note on Algorithmic Trading based on Some Personal Experience
[ 講演概要 ]
I overview a brief history of HFT based on my 14 years' personal experience of the algorithmic trading business at a wall-street company. Starting with descriptions about layers of the algo business, I mention a stochastic index arbitrage business that I employed in some detail. After reviewing some HFT specific issues such as super short-period alpha, I try to forecast what is going on with HFT in near future.



16:45-18:15   数理科学研究科棟(駒場) 122号室
小沢登高 氏 (京大数理研)
The Furstenberg boundary and $C^*$-simplicity


14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
岩田繁英 氏 (東京海洋大学大学院海洋科学技術研究科)
[ 講演概要 ]



15:30-17:00   数理科学研究科棟(駒場) 122号室
石川大蔵 氏 (早稲田)
Rank 2 weak Fano bundles on cubic 3-folds (日本語)
[ 講演概要 ]
A vector bundle on a projective variety is called weak Fano if its
projectivization is a weak Fano manifold. This is a generalization of
Fano bundles.
In this talk, we will obtain a classification of rank 2 weak Fano
bundles on a nonsingular cubic hypersurface in a projective 4-space.
Specifically, we will show that there exist rank 2 indecomposable weak
Fano bundles on it.


16:50-18:20   数理科学研究科棟(駒場) 128号室
星野 壮登 氏 (東京大学大学院数理科学研究科)
[ 講演概要 ]



17:00-18:30   数理科学研究科棟(駒場) 002号室
荒野悠輝 氏 (東大数理)
Unitary spherical representations of Drinfeld doubles (JAPANESE)
[ 講演概要 ]
It is known that the Drinfeld double of the quantized
enveloping algebra of a semisimple Lie algebra looks similar to the
quantized enveloping algebra of the complexification of the Lie algebra.
In this talk, we investigate the unitary representation theory of such
Drinfeld double via its analogy to that of the complex Lie group.
We also talk on an application to operator algebras.



16:45-18:15   数理科学研究科棟(駒場) 122号室
John F. R. Duncan 氏 (Case Western Reserve Univ.)
Vertex operator algebras in umbral Moonshine


17:00-18:00   数理科学研究科棟(駒場) 056号室
長町一平 氏 (東京大学数理科学研究科)
On a good reduction criterion for polycurves with sections (Japanese)



17:00-18:30   数理科学研究科棟(駒場) 122号室
小木曽岳義 氏 (城西大学)
Clifford quartic forms の局所関数等式とhomaloidal EKP-polynomials
[ 講演概要 ]
局所関数等式が正則概均質ベクトル空間の基本相対不変式とその双対空間の多項式のペアから与えられることは知られている。我々は Clifford quartic form と呼ばれるある4次斉次多項式を構成し, それが概均質ベクトル空間の相対不変式ではないにも関わらず局所関数等式を満たすことを示した。局所関数等式を満たす多項式を特徴付ける問題は興味深い未解決問題であるが, この問題に関連し、 Etingof, Kazhdan, Polishchuk は(もっと一般的な設定で)ある予想を提示した。我々は、 Clifford quartic form を用いて, この予想に反例があることを示した。 (この講演は佐藤文広氏との共同研究に基づいている。)


17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : 16:30-17:00 Common Room
久我 健一 氏 (千葉大学)
Introduction to formalization of topology using a proof assistant. (JAPANESE)
[ 講演概要 ]
Although the program of formalization goes back to David
Hilbert, it is only recently that we can actually formalize
substantial theorems in modern mathematics. It is made possible by the
development of certain type theory and a computer software called a
proof assistant. We begin this talk by showing our formalization of
some basic geometric topology using a proof assistant COQ. Then we
introduce homotopy type theory (HoTT) of Voevodsky et al., which
interprets type theory from abstract homotopy theoretic perspective.
HoTT proposes "univalent" foundation of mathematics which is
particularly suited for computer formalization.



10:30-12:00   数理科学研究科棟(駒場) 126号室
久本 智之 氏 (名古屋大学)
On uniform K-stability (Japanese)
[ 講演概要 ]
It is a joint work with Sébastien Boucksom and Mattias Jonsson. We first introduce functionals on the space of test configurations, as non-Archimedean analogues of classical functionals on the space of Kähler metrics. Then, uniform K-stability is defined as a counterpart of K-energy's coercivity condition. Finally, reproving and strengthening Y. Odaka's results, we study uniform K-stability of Kähler-Einstein manifolds.


15:30-17:00   数理科学研究科棟(駒場) 122号室
松本雄也 氏 (東大数理)
Good reduction of K3 surfaces (日本語 or English)
[ 講演概要 ]
We consider degeneration of K3 surfaces over a 1-dimensional base scheme
of mixed characteristic (e.g. Spec of the p-adic integers).
Under the assumption of potential semistable reduction, we first prove
that a trivial monodromy action on the l-adic etale cohomology group
implies potential good reduction, where potential means that we allow a
finite base extension.
Moreover we show that a finite etale base change suffices.
The proof for the first part involves a mixed characteristic
3-dimensional MMP (Kawamata) and the classification of semistable
degeneration of K3 surfaces (Kulikov, Persson--Pinkham, Nakkajima).
For the second part, we consider flops and descent arguments. This is a joint work with Christian Liedtke.
[ 講演参考URL ]


16:50-18:20   数理科学研究科棟(駒場) 128号室
北別府 悠 氏 (京都大学大学院理学研究科)
A finite diameter theorem on RCD spaces



16:00-17:00   数理科学研究科棟(駒場) 056号室
Tea:15:30~16:00 コモンルーム
Gunnar Carlsson  氏 (Stanford University, Ayasdi INC)
The Shape of Data
[ 講演概要 ]
There is a tremendous amount of attention being paid to the notion of
"Big Data". In many situations, however, the problem is not so much the
size of the data but rather its complexity. This observation shows that
it is now important to find methods for representing complex data in a
compressed and understandable fashion. Representing data by shapes
turns out to be useful in many situations, and therefore topology, the
mathematical sub discipline which studies shape, becomes quite
relevant. There is now a collection of methods based on topology for
analyzing complex data, and in this talk we will discuss these methods,
with numerous examples.
[ 講演参考URL ]



17:30-18:30   数理科学研究科棟(駒場) 056号室
Shou-Wu Zhang 氏 (Princeton University)
Colmez' conjecture in average (English)
[ 講演概要 ]
This is a report on a joint work with Xinyi Yuan on a conjectured formula of Colmez about the Faltings heights of CM abelian varieties. I will sketch a deduction of this formula in average of CM types from our early work on Gross-Zagier formula. When combined with a recent work of Tsimerman, this result implies the Andre-Oort conjecture for the moduli of abelian varieties.
Our method is different than a recently announced proof of a weaker form of the average formula by Andreatta, Howard, Goren, and Madapusi Pera: we use neither high dimensional Shimura varieties nor Borcherds' liftings.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)


16:45-18:15   数理科学研究科棟(駒場) 122号室
磯野優介 氏 (京大数理研)
Unique prime factorization and bicentralizer problem for a class of type III factors



10:30-11:30   数理科学研究科棟(駒場) 056号室
山田澄生 氏 (学習院大学)
Convex bodies and geometry of some associated Minkowski functionals (日本語)
[ 講演概要 ]
In this talk, we will investigate the construction of so-called Hilbert metric, as well as Funk metric, defined on convex set from a new variational viewpoint. The local and global aspects of the geometry of the resulting Minkowski functionals will be contrasted. As an application, some remarks on the Perron-Frobenius theorem will be made. Part of the project is a joint work with Athanase Papadopoulos (Strasbourg).


17:00-18:30   数理科学研究科棟(駒場) 122号室
Anton Evseev 氏 (University of Birmingham)
RoCK blocks, wreath products and KLR algebras (English)
[ 講演概要 ]
The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.


17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : 16:30-17:00 Common Room
加藤 晃史 氏 (東京大学大学院数理科学研究科)
Quiver mutation loops and partition q-series (JAPANESE)
[ 講演概要 ]
Quivers and their mutations are ubiquitous in mathematics and
mathematical physics; they play a key role in cluster algebras,
wall-crossing phenomena, gluing of ideal tetrahedra, etc.
Recently, we introduced a partition q-series for a quiver mutation loop
(a loop in a quiver exchange graph) using the idea of state sum of statistical
mechanics. The partition q-series enjoy some nice properties such
as pentagon move invariance. We also discuss their relation with combinatorial
Donaldson-Thomas invariants, as well as fermionic character formulas of
certain conformal field theories.
This is a joint work with Yuji Terashima.



10:30-12:00   数理科学研究科棟(駒場) 126号室
足立 真訓 氏 (東京理科大学)
On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)
[ 講演概要 ]
We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR manifolds.


15:30-17:00   数理科学研究科棟(駒場) 122号室
Will Donovan 氏 (IPMU)
Twists and braids for general 3-fold flops (English)
[ 講演概要 ]
When a 3-fold contains a floppable rational curve, a theorem of Bridgeland provides a derived equivalence between the 3-fold and its flop. I will discuss recent joint work with Michael Wemyss, showing that these flop functors satisfy Coxeter-type braid relations. Using this result, we construct an action of a braid-type group on the derived category of the 3-fold. This group arises from the topology of a certain simplicial hyperplane arrangement, determined by the local geometry of the curve. I will give examples and explain key elements in the construction, including the noncommutative deformations of curves introduced in our previous work.
[ 講演参考URL ]


16:30-18:00   数理科学研究科棟(駒場) 056号室
尾崎克久 氏 (芝浦工業大学システム理工学部)
[ 講演概要 ]

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