Nearby cycles and derived geometry - Revision history

Brv60445 at 09:50, 18 March 2024

2024-03-18T09:50:19Z

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	= Conference: Nearby Cycles and Derived Geometry (Feb 26 - Mar 1 2024)=		= Conference: Nearby Cycles and Derived Geometry (Feb 26 - Mar 1 2024)=
			__TOC__

			==Aim and Scope==
			The geometry of nearby cycles, using microlocal methods or motivic approaches, has recently seen spectacular advances in many different directions: symplectic geometry, non-archimedean analytic geometry, or arithmetic geometry, using more and more tools from derived algebraic geometry and higher category theory. This has many applications in mirror symmetry, in the Langlands program, or in ramification theory, for instance. This conference aims at gathering experts from different fields to emulate progress in different branches of geometry.
			<br>
	==List of Speakers==		==List of Speakers==
	*Tomoyuki Abe		*Tomoyuki Abe

Brv60445 at 09:49, 18 March 2024

2024-03-18T09:49:47Z

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 <div class="res-img">[[File:Donau-Regensburg-St_Oswald.jpg|1100px|center]]</div>
 =&nbsp;Conference: Nearby Cycles and Derived Geometry (Feb 26 - Mar 1 2024)=
 ==List of Speakers==
 *Tomoyuki Abe

Brv60445 at 09:49, 18 March 2024

2024-03-18T09:49:27Z

← Older revision		Revision as of 11:49, 18 March 2024
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	= Conference: Nearby Cycles and Derived Geometry (Feb 26 - Mar 1 2024)=		= Conference: Nearby Cycles and Derived Geometry (Feb 26 - Mar 1 2024)=
			<br>
			<b>Welcome to Women in Mathematics in Regensburg!<b>
			<br>
			The goal of this group is to promote and support the participation and advancement of women , and other unrepresented people, in the field of mathematics in Regensburg.
			We would like to create a network of women mathematicians and to provide resources and support for their academic and professional development. We also aim to raise awareness of the importance of diversity and inclusion in mathematics and to foster a supportive and welcoming environment for all women in the field.
			Through our events, workshops and other resources, we hope to pursue careers in mathematics and to provide a supportive community for those who are already in the field.
			Hence everyone with an interest in mathematics, such as bachelor and master students, PhD students and more advanced positions in or outside academia, but also everyone from any other subject who is interested in math is very welcomed to join.
			Our group is waiting for you!
			Explore our website to discover more about our activities and how to participate!

			[[User:Brv60445\|Brv60445]] ([[User talk:Brv60445\|talk]])


			“The initiative is supported by the Fakultät für Mathematik of the Universität Regensburg, by the SBF 1085 "Higher Invariants", and by the RTG 2339 " Interfaces, Complex Structures, and Singular Limits".

Hom54528 at 12:55, 5 March 2024

2024-03-05T12:55:40Z

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	The key notion is that of a compactly assembled additive infinity-category and its continuous stabilization. I will explain how to define continuous K-theory of compactly assembled additive categories. In the above example my result about the identification of K^cont(Nuc(R)) with lim_n K(R/I^n) can be interpreted as commutation of K-theory with the inverse limit for the sequence (Flat-R/I^n)_n of compactly assembled additive categories of flat modules.		The key notion is that of a compactly assembled additive infinity-category and its continuous stabilization. I will explain how to define continuous K-theory of compactly assembled additive categories. In the above example my result about the identification of K^cont(Nuc(R)) with lim_n K(R/I^n) can be interpreted as commutation of K-theory with the inverse limit for the sequence (Flat-R/I^n)_n of compactly assembled additive categories of flat modules.

	~~==Streaming Information==~~
	~~The conference will be streamed on Zoom:~~

	~~'''Zoom link:''' https://uni-regensburg.zoom-x.de/j/64299765249?pwd=T2thQ2JnVmp3bTRuU3hoRmtTVDdhUT09~~

	~~'''Meeting ID:''' 642 9976 5249~~

	~~'''Password:''' nearby~~
	~~<br>~~
	==Registration==		==Registration==
	'''Pre-Registration:''' Registration for in-person attendance is closed. <br>		'''Pre-Registration:''' Registration for in-person attendance is closed. <br>

Hek43333 at 07:30, 28 February 2024

2024-02-28T07:30:09Z

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	<br>		<br>
	==Conference Picture==		==Conference Picture==
			<div class="res-img">[[File:NC_Konferenz.JPG\| center]]</div>
	<br>		<br>
	==Sponsors of the conference==		==Sponsors of the conference==
	This conference is funded by '''SFB 1085 "Higher Invariants"'''		This conference is funded by '''SFB 1085 "Higher Invariants"'''

Cid36224 at 23:31, 26 February 2024

2024-02-26T23:31:59Z

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	\| <b>Alberto Vezzani</b>		\| <b>Alberto Vezzani</b>
	\| <b>Massimo Pippi</b>		\| <b>Massimo Pippi</b>
	\| <b>Yuri Yatagawa</b>		\| <b>Yuri Yatagawa</b><br>(online talk)
	\|-		\|-
	\| style="text-align:center;" \|10:30 - 11:00		\| style="text-align:center;" \|10:30 - 11:00

Cid36224 at 19:40, 26 February 2024

2024-02-26T19:40:04Z

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	I will discuss some duality theorems for p-adic proétale cohomology of analytic spaces. The duality results follow from de Rham dualities after applying a comparison theorem that allows to express proétale cohomology as a filtered Frobenius eigenspace of the de Rham cohomology. This comparison theorem comes from a local computation of the p-adic nearby cycles computing the p-adic proétale cohomology. This is based on a joint work with Pierre Colmez and Wieslawa Niziol.		I will discuss some duality theorems for p-adic proétale cohomology of analytic spaces. The duality results follow from de Rham dualities after applying a comparison theorem that allows to express proétale cohomology as a filtered Frobenius eigenspace of the de Rham cohomology. This comparison theorem comes from a local computation of the p-adic nearby cycles computing the p-adic proétale cohomology. This is based on a joint work with Pierre Colmez and Wieslawa Niziol.

	'''Benjamin Hennion: ~~tba~~'''
			'''Benjamin Hennion: Singularity invariants glued on (-1)-shifted symplectic schemes'''

			We will explain how to glueing singularity invariants from local models of moduli spaces endowed with a (-1)-shifted symplectic structure. By studying the moduli of such local models, we will explain how to recover Brav--Bussi--Dupont--Joyce--Szendroi's perverse sheaf categorifying the DT-invariants, as well as a strategy for glueing more evolved singularity invariants, such as matrix factorizations.


	'''Fangzhou Jin: The limit and boundary characteristic classes in Borel-Moore motivic homology'''		'''Fangzhou Jin: The limit and boundary characteristic classes in Borel-Moore motivic homology'''

Cid36224 at 17:07, 25 February 2024

2024-02-25T17:07:54Z

← Older revision		Revision as of 19:07, 25 February 2024
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	*Martin Gallauer		*Martin Gallauer
	*Sally Gilles		*Sally Gilles
			*Benjamin Hennion
	*Haoyu Hu		*Haoyu Hu
	*Fangzhou Jin		*Fangzhou Jin
Line 24:		Line 25:
	*Hiro Lee Tanaka		*Hiro Lee Tanaka
	*Alberto Vezzani		*Alberto Vezzani
	*Gabriele Vezzosi
	*Enlin Yang		*Enlin Yang
	*Yuri Yatagawa <br>		*Yuri Yatagawa <br>
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	\| style="padding: 20px"\|15:30 - 16:30		\| style="padding: 20px"\|15:30 - 16:30
	\|<b>Charanya Ravi</b>		\|<b>Charanya Ravi</b>
	\|<b>~~Gabriele Vezzosi~~</b>		\|<b>Benjamin Hennion</b>
	\|		\|
	\|<b>Haoyu Hu</b>		\|<b>Haoyu Hu</b>
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	I will discuss some duality theorems for p-adic proétale cohomology of analytic spaces. The duality results follow from de Rham dualities after applying a comparison theorem that allows to express proétale cohomology as a filtered Frobenius eigenspace of the de Rham cohomology. This comparison theorem comes from a local computation of the p-adic nearby cycles computing the p-adic proétale cohomology. This is based on a joint work with Pierre Colmez and Wieslawa Niziol.		I will discuss some duality theorems for p-adic proétale cohomology of analytic spaces. The duality results follow from de Rham dualities after applying a comparison theorem that allows to express proétale cohomology as a filtered Frobenius eigenspace of the de Rham cohomology. This comparison theorem comes from a local computation of the p-adic nearby cycles computing the p-adic proétale cohomology. This is based on a joint work with Pierre Colmez and Wieslawa Niziol.

			'''Benjamin Hennion: tba'''
	'''~~Gabriele Vezzosi~~: ~~Analogs of Beilinson-Drinfeld's Grassmannian on a surface'~~''

	~~Beilinson-Drinfeld~~'~~s Grassmannian on an algebraic curve is an important~~
	~~object in Representation Theory and in the Geometric Langlands Program.~~
	~~I will describe some analogs of this construction when the curve is replaced by a surface,~~
	~~together with related preliminary results.~~
	~~This is partly a joint work with Benjamin Hennion (Orsay) and Valerio Melani (Florence),~~
	~~and partly a joint work in progress with Andrea Maffei (Pisa) and Valerio Melani (Florence).~~


	'''Fangzhou Jin: The limit and boundary characteristic classes in Borel-Moore motivic homology'''		'''Fangzhou Jin: The limit and boundary characteristic classes in Borel-Moore motivic homology'''

Hom54528 at 11:51, 23 February 2024

2024-02-23T11:51:57Z

← Older revision		Revision as of 13:51, 23 February 2024
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	==Streaming Information==		==Streaming Information==
	The conference will be streamed on Zoom~~. The~~ Zoom link ~~will be posted here before the start of the conference~~.		The conference will be streamed on Zoom:

			'''Zoom link:''' https://uni-regensburg.zoom-x.de/j/64299765249?pwd=T2thQ2JnVmp3bTRuU3hoRmtTVDdhUT09

			'''Meeting ID:''' 642 9976 5249

			'''Password:''' nearby
	<br>		<br>
	==Registration==		==Registration==

Hom54528 at 19:54, 19 February 2024

2024-02-19T19:54:57Z

← Older revision		Revision as of 21:54, 19 February 2024
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	In this talk, we will sketch the construction of non-acyclicity classes for constructible etale sheaves on (not necessarily smooth) varieties, which is defined in a recent joint work with Yigeng Zhao. This cohomological class is supported on the non-locally acyclicity locus. As applications, we show that the Milnor formula and Bloch's conductor formula can be reformulated in terms of the functorial properties of non-acyclicity classes. Based on this formalism, we propose a Milnor type formula for non-isolated singularities.		In this talk, we will sketch the construction of non-acyclicity classes for constructible etale sheaves on (not necessarily smooth) varieties, which is defined in a recent joint work with Yigeng Zhao. This cohomological class is supported on the non-locally acyclicity locus. As applications, we show that the Milnor formula and Bloch's conductor formula can be reformulated in terms of the functorial properties of non-acyclicity classes. Based on this formalism, we propose a Milnor type formula for non-isolated singularities.


			'''Tomoyuki Abe: Characteristic cycles of l-adic sheaves and A^1-homotopy'''

			The characteristic cycle of an l-adic sheaf was defined by T. Saito after Beilinson's definition (and existence) of singular support.
			In the positive characteristic situation, the singular support is defined as a middle dimensional conic closed subset of the cotangent space, but not necessarily be Langrangian.
			This deficit makes is hard to show the Grothendieck-Riemann-Roch type result for characteristic cycle.
			In this talk, I will show such a result after inverting the characteristic of the base field using A^1-homotopy theory.