2008-2018年

関連しそうなセミナーや研究集会の予定を随時掲載していきます。

2018年1月31日（水）埼玉大学木曜セミナー

16:00 -- 17:00　場所:数学研究室1（理工学研究科棟5階）

一木俊助氏(横浜国立大学)

On transversality lemmas

トムの横断性定理などの横断性に関する諸結果は, 安定写像やジェネリックな写像の研究等, いわゆる大域的特異点論の研究には不可欠な道具であるといえる. 様々な状況における横断性定理を導く際の基本的な道具として「the fundamental transversality lemma」とよばれる古くから知られた重要な補題があるが, John N. Matherは, その補題の仮定を大幅に緩めた結果を導いた. そして, 講演者はそのMatherの結果の仮定を更に緩め, その仮定と結論が必要十分になるところまで拡張を行った. 本講演では, これらの結果をご紹介する.

Mon 25 Sep 2017 - Fri 29 Sep 2017: the 7th Japanese-Australian Workshop on Real and Complex Singularities, to be held in Sydney; at the University of Sydney, ABS Seminar Room 3003.; First Announcement of JARCS VII,
Dear Colleagues,
This is the first announcement of the 7th Japanese-Australian Workshop on Real and Complex Singularities, to be held in Sydney Mon 25 Sep 2017 - Fri 29 Sep 2017, at the University of Sydney, ABS Seminar Room 3003. Early next year we will set up our web page and ask for expressions of interest. We welcome your participation to our workshop and if you know anyone interested please let them know. In the meantime have a Happy and Prosperous New Year!
Laurentiu.

Sun 10　Sep 2017 - Sat　16　Seo　2017: Geometric and Algebraic Singularity Theory; The Mathematical Research and Conference Center Bedlewo, Poland; Organiser: Wojciech Domitrz, Toru Ohmoto, Takahiro Yamamoto, Masatomo Takahashi, Ewa Strozyna, Zaneta Trebska, Mariusz Zajac, Michal Zwierzynski

2017年6月8日埼玉大学木曜セミナー: 場所:数学研究室1（理工学研究科棟5階）; 13:30-14:30: Ricardo Uribe-Vargas, Université de Bourgogne; Support function, big front singularities and duality.; 　Abstract: The so-called "support function" of a given closed convex plane curve enables to describe the equidistant curves and their singularities. We show that the graph of the support function contains all local and global geometric information of the initial curve, of its equidistants and of its evolute (caustic). To any plane curve (without convexity restrictions) corresponds a curve on the unit cylinder (the graph of a "multivalued support function") and vice-versa. We define the "support map", which sends any plane curve to a curve on the unit cylinder and establish the correspondence between Euclidean differential geometry of plane curves and projective differential geometry of curves on the unit cylinder.
We geometrically construct the natural isomorphism between the front (in space-time) formed by the union of equidistants of a plane curve and the dual surface of its corresponding curve on the cylinder (the subvariety formed by the planes of $R^3$ which are tangent to this space curve). Our results hold in Euclidean spaces of higher dimensions for submanifolds of any dimension.
A corollary of our construction is the following:
Theorem. For any class of singularities $X$ (for example, $A, D, E$) the set of singularities of type $X$ of the evolute of a smooth submanifold $M$ of $R^n$ is isomorphic to the set of singularities of type $X$ in the front formed by the hyperplanes of $R^{n+1}$ which are tangent to the image of $M$ by the support map (in the unit cylinder $C_n\subset R^{n+1}$) by the support map.

2017年6月1日-3日: 微分幾何学と特異点論の応用（世話人　高橋雅朋, 長谷川大）; 岩手医科大学創立６０周年記念館(盛岡市)

2017年2月15日-16日: ホモトピー論と特異点論小研究集会【島川先生・村山先生退職記念】; 北海道大学理学部３号館3-307室

2017年1月12日（木）埼玉大学木曜セミナー: 場所:数学研究室1（理工学研究科棟5階）; 15:00--16:00 神戸祐太（埼玉大学M2）; Construction of the moduli space of reduced Gr¨obner bases; アブストラクト k を係数環としてもつ多項式環において固定された先頭項集合をもつ被約 Gr¨obner 基底のモジュライ空間が点のヒルベルトスキームの局所閉スキームとして構成された. 今回はその一般化として解が有限個でない場合にも固定された先頭項集合をもつ被約 Gr¨obner 基底のクラスを適切に制限したモジュライ空間を構成する. また, そのモジュライ空間が原点で非特異であることがアフィン空間になることと同値であることや, 閉部分スキームとして先頭項集合を固定した “斉次” 被約 Gr¨obner 基底のモジュライ空間が構成できること, および具体的な計算例を紹介する.; 参考文献; [Led11] Mathias Lederer, Gr¨obner strata in the Hilbert scheme of points, J.Commut. Algebra 3 (2011), no. 3, 349-404.; [Rob09] L. Robbiano, On border basis and Gr¨obner basis schemes, Collect. Math. 60 (2009), no. 1, 11-25. MR MR2490747; 16:00--16:20 Tea and coffee; 16:20--17:20 Jean-Baptiste Campesato (Saitama University, JSPS post doc fellow),; Motivic integration and real singularities

2016年11月24日（木）埼玉大学木曜セミナー

場所:数学研究室1（理工学研究科棟5階）

14:30-15:30: Jean-Baptiste Campesato (Saitama University, JSPS Post doc fellow)

On a motivic invariant of the arc-analytic equivalence

　Abstract: The first part of this talk is devoted to the arc-analytic equivalence which is an equivalence relation on Nash function germs (i.e. real analytic function germs which are semialgebraic).
Next, to a Nash function germ we associate a motivic zeta function whose construction is analog to the one of Denef--Loeser. This is a formal power series with coefficients in a Grothendieck ring of $\mathcal{AS}$-sets up to $\mathbb{R}^*$-equivariant $\mathcal{AS}$-bijections over $\mathbb{R}^*$, a real analog of the Grothendieck ring of G. Guibert, F. Loeser and M. Merle. This zeta function is an invariant of the arc-analytic equivalence.
This zeta function generalizes the previous construction of G. Fichou. Its extra structure allows us to get a convolution formula from which we derive a partial classification of Brieskorn polynomials by showing that the arc-analytic type of a Brieskorn polynomial determines its exponents.

2016年6月22日（水）より24日（金）まで

第７回神戸特異点研究会

兵庫教育大学神戸ハーバーランドキャンパス

(案内）

2016年6月2日（木）午後より4日（土）午前まで: 研究集会「トポロジー・特異点論とその応用」; 場所：青山学院大学相模原キャンパス D棟

2016年4月21日（木）埼玉大学木曜セミナー: 場所:数学研究室1（理工学研究科棟5階）; 16:20-17:20: Carles Bivia Ausina (Universitat Politecnica de Valencia); Log-canonical threshold, diagonal ideals and mixed multiplicities; : Abstract: We characterize the ideals $I$ of finite colength of the ring $\mathcal O_n$ of complex analytic functions germs $(\mathbb C^n,0)\to \mathbb C$ whose integral closure is equal to the integral closure of an ideal generated by pure monomials. The computation of the integral closure of a given ideal is an important problem both in commutative algebra and singularity theory. The mentioned characterization, which is motivated by an inequality proven by Demailly and Pham, is given in terms of the log canonical threshold of $I$ and the sequence of mixed multiplicities of $I$. Motivated by a result of Hickel, we relate this topic with the question of characterizing the ideals of $\mathcal O_n$ whose multiplicity is equal to the product of their mixed \L ojasiewicz exponents and derive some consequences of our study to singularities of function germs.; before we have the following; 13:00-15:00: Informal seminar on tropical geometry (by Cristina Valle); 15:00-16:00: Duality, Eisenbud-Levine's theorem and Gorenstein property (by Keita Suyama, Saitama University); We have the seminar dinner after.

2016年3月12日(土)，3月13日(日): Encounter with Mathematics 第66回　幾何学と特異点の出会い

2016年2月20日(土)，2月21日(日): Encounter with Mathematics 第64回　複素解析と特異点　－留数が解き明かす特異点の魅力－

2015年11月23日（月）より27日（金）まで: 第六回日豪実・複素特異点研究集会(The sixth Australian-Japanese Workshop on Real and Complex Singularities); 鹿児島大学