News

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2/4/15

Research positions 2015/16

at Eduard Čech Institute for Algebra, Geometry and Physics in Brno, Prague or Opava in Czech Republic.

The Eduard Čech center had been established in 2005 and, since 2012, it continues as a national research center focusing its attention to the interaction between algebra, geometry, and mathematical physics. The participating institutions are the Faculty of Science of Masaryk University in Brno, the Faculty of Mathematics and Physics of the Charles University in Prague, the Institute of Physics of the Academy of Sciences of the Czech Republic and the Mathematics Institute of the Silesian University in Opava (see also eci.math.muni.cz).

The Center invites applications for several research positions commencing during the academic year 2015/2016 at the date depending on mutual agreement. The positions are initially for one year with a possibility of extension. The candidates must be recent PhD's and should submit a letter of application accompanied by a CV, list of publications and an outline of their research project to Professor Jiri Rosicky (rosicky@math.muni.cz) not later than

March 15, 2015.

They should also arrange for at least 2 letters of recommendation (one can be from a Czech mathematician) to be mailed directly to rosicky@math.muni.cz before March 15, 2015. The successful applicants will be notified as soon as possible but not later than April 30, 2015.

10/25/13

Seminar talks on Thursday, November 7, 2013:

  • 9.30am, seminar room of Department of Algebra
    Roger Wiegand: Torsion in tensor products and vanishing of Tor.
    Abstract in PDF »

  • 2.00pm, seminar room of Department of Algebra
    Sylvia Wiegand: Prime ideals in Noetherian polynomial and power series integral domains.
    Abstract in PDF »
10/25/13

ECI seminar on Monday, November 4, 2013:

H.-C. Herbig (ECI): Open and solved problems in singular Poisson geometry.

November 4, at 3.30pm in the seminar room of Dept. Alg.

Abstract: I will talk about applications of the BFV-complex to deformation quantization of singular symplectic quotients. I will indicate why it is necessary to develop a cohomology theory for Lie-Rinehart pairs (A,L) that encompasses also the case when the the A-module underlying the Lie algebra L is non-projective.

10/9/13

Joint ECI-AMeGA workshop

A joint ECI-AMeGA workshop takes place in Třešť on October 11-12, 2013. More information »

9/12/13

Extra Events on 15.8.

  • 10:00, seminar room of Department of Algebra
    Igor Kříž: The Quillen-Suslin theorem for the ordered configuration space of n points in A1
  • 14:00 6th MATHEMATICAL COLLOQUIUM, room K1
    Igor Kříž: Super-modular functors and their K-theoretic realizations
  • 15:30, seminar room of Department of Algebra
    Po Hu: Field theories, stable homotopy theory and Khovanov homology
6/11/13

ECI Workshop of Algebra

Friday, June 14, Masarykova Univerzita Brno, room M5



10.00 - 10.30Coffee break
10.30 - 11.30Šťovíček, Generalized Hill lemma
11.30 - 12.00Trlifaj (Co)tilting, (co)filtrations, and (co)localization."
12.00 - 13.00Lunch
13.00 - 13.30Rosický, Shelah's singular compactness theorem
13.30 - 14.00Raventos, Stabilization of quasicategories
14.00 - 14.30Bourke, TBA
14.30 - 15.00Coffee break
15.00 - 18.00Discussion


Changes are possible

5/7/13

I. Kříž (Univ. of Michigan) : Elliptic cohomology

Friday 10.5. 10:40 at Seminar room of MUUK

Abstract: I will briefly introduce the idea of elliptic cohomology, how it is constructed and why the topic is still alive mathematically. The last part concerns conjectured connections with analysis and geometry which have not been established so far, even though several attempts have been made.

More info at: http://muuk.karlin.mff.cuni.cz/cs/node/13

4/29/13

Call For Research Positions 2013/14

Eduard Čech Institute for Algebra, Geometry and Physics

The Eduard Čech center had been established in 2005 and, since 2012, it continues as a national research center focusing its attention to the interaction between algebra, geometry, and mathematical physics. The participating institutions are the Faculty of Science of Masaryk University in Brno, the Faculty of Mathematics and Physics of the Charles University in Prague, the Institute of Physics of the Academy of Sciences of the Czech Republic and the Mathematics Institute of the Silesian University in Opava.

The Center invites applications for several research positions commencing during the academic year 2013/2014 at the date depending on mutual agreement. The positions are initially for one year with a possibility of extension. The candidates must be recent PhD's and should submit a letter of application accompanied by a CV, list of publications and an outline of their research project to Professor Jiri Rosicky (rosicky@math.muni.cz) not later than

May 15, 2013

They should also arrange for at least 2 letters of recommendation (one can be from a Czech mathematician) to be mailed directly to rosicky@math.muni.cz before May 15, 2013. The successful applicants will be notified as soon as possible but not later than June 30, 2013.

3/4/13

A new seminar: Seminář o topologických teoriích pole (J. Šťovíček)

More info here.

12/17/12

Brauer-Thrall Theorems and Conjectures for Commutative Local Rings

(2nd ECI COLLOQUIUM)

Roger Wiegand
University of Nebraska
December 17, 2012, 5:20 pm, K3

The Brauer-Thrall Conjectures, now theorems, were originally formulated in terms of representations of finite-dimensional algebras. They say, roughly speaking, that failure of finite representation type entails the existence of lots of indecomposable representations of large dimension. These conjectures have been successfully transplanted to the representation theory of commutative local rings. This talk will be a survey of such results, conjectures and counterexamples, for various categories of finitely generated modules over a commutative Noetherian local ring. The emphasis will be on maximal Cohen-Macaulay modules over Cohen-Macaulay local rings.

12/4/12

Algebraic seminar upcomings

  • 10.12. Tibor Beke (University of Massachusets):
    A functorial version of Shelah's Singular Compactness

    Abstract: Shelah's celebrated singular compactness theorem asserts that if G is a group whose cardinality is singular, and all subgroups of G are free, then G itself is free. Shelah's proof can be adapted to various other settings, including abelian groups, R-modules, filtered R-modules, colorings of infinite graphs, and transversals of systems of sets. It hasn't been clear whether there is a single statement unifying these applications and their various conclusions. This talk is a preliminary report on joint work with J. Rosicky on what seems to be the "most comprehensive" form of singular compactness. The proof is an adaptation of one of Shelah's arguments to the setting of accessible categories and functors.

  • 17.12. Sylvia Wiegand (University of Nebraska):
    Prime ideals in Noetherian rings

    Abstract: Let R be a commutative Noetherian ring. We consider the set Spec(R) of prime ideals of R as a partially ordered set, ordered by inclusion. Around 1950 Irving Kaplansky asked, "Which partially ordered sets arise as Spec(R) for some Noetherian ring R?" This question is completely open, even if only two-dimensional sets are considered, despite a large amount of work over the intervening years by many mathematicians, such as Hochster, Heitmann, Nagata, McAdam, and Ratli . In this talk, we describe prime spectra for some two-dimensional rings of polynomials and power series. This involves our work and work of William Heinzer, Christel Rotthaus, Roger Wiegand and our students.

  • 19.12. Vitězslav Kala (MFF UK and Purdue University):
    Asymptotic results in the Langlands program

    Abstract: The Langlands program is a series of conjectures that provide a common framework for a large part of modern number theory. Its goal is to relate representations of absolute Galois groups of number fields to certain analytic objects, automorphic representations. For example, a special case of this correspondence was proved by Wiles and Taylor as the main step of the proof of Fermat's Last Theorem.
    In the talk, we will first give an overview and a motivation for the Langlands program, keeping the prerequisited minimal. Then we will discuss some recent asymptotic results on the number of various types of Galois and automorphic representations.
11/5/12

Public Lecture

Prof. Reza Choudary (Abdus Salam School of Math. Sciences, Lahore) - A School of Different Type

Friday 9.11., 14:00 - 15:00, Refectory, Malostranské nám. 25
11/5/12

Lecture notes in D-modules

For those who are concerned here you can download lecture notes in D-modules by Libor Křižko containing topics of ECI seminars on D-modules from 2011/12.

Thank you Libor.

11/5/12

Seminars on Algebraic Microlocal Analysis

Pierre Schapira

TALK 1: Characteristic variety and microsupport

Monday 5.11., 15:30-16:30, seminar room of Dept. of Algebra

On a complex manifold X, a coherent D-module M admits a characteris­tic variety char(M), a closed conic co-isotropic complex subvariety of the cotangent bundle T*X. On a real manifold M, a sheaf admits a micro-support SS(F), a closed conic co-isotropic subset of the cotangent bundle T*M. In this talk, I will explain both constructions, describe their functorial properties and explain their links.

TALK 2: Index theorem for elliptic pairs

Wednesday 7.11., 11:30 - 12:30, seminar room of MU UK

On a complex manifold (X, O_X), an elliptic pair (M ,F) is the data of a co­herent D-module M and an R-constructible sheaf F satisfying the following ellipticity condition: the intersection char(M ) \cap SS(F) is contained in the zero-section of T*X. I will first explain how to recover the classical regu­larity and .niteness theorems of elliptic systems. Then, I will give an index theorem and explain the link with the classical Riemann-Roch-Grothendieck and Atiyah-Singer theorems.

TALK 3: The subanalytic site. Applications to irregular D-modules

Friday 9.11., 13:00 - 14:00, Refectory, Malostranské nám. 25

I will first recall the construction of the sheaves of holomorphic functions with temperate growth or with exponential decay. These are not sheaves on the usual topology, but sheaves on the subanalytic site. Then I will explain how these objects appear naturally in the study of irregular holonomic D-modules.

References
  • [1] M. Kashiwara and P. Schapira, Sheaves on Manifolds, Grundlehren der Math. Wiss. 292 Springer-Verlag (1990).
  • [2] , Ind-sheaves, Astrisque, Soc. Math. France, 271 (2001)
  • [3] , Microlocal Euler classes and Hochschild homology, math.arXiv:1203.4869
  • [4] M. Sato, T. Kawai and M. Kashiwara, Microfunctions and pseudo-di.erential equations, in Komatsu (ed.), Hyperfunctions and pseudo-di.erential equations, Proceedings Katata 1971, Lecture Notes in Math. Springer-Verlag 287 p. 265–529 (1973).
  • [5] P. Schapira, Triangulated categories for the analysts, in ”Triangulated categories” London Math. Soc. LNS 375 Cambridge University Press, pp 371-389 (2010)
  • [6] , Three lectures on Algebraic Microlocal Analysis, math.arXiv:1206.1435 [ScSn94] P. Schapira and J-P. Schneiders, Index theorem for elliptic pairs, Ast´erisque Soc. Math. France 224 (1994)
10/29/12

Colloquium: Algebraic Microlocal Analysis

Pierre Schapira

Thursday 8.11., 13:00-14:00 at K1 lecture room

To any sheaf F on a real manifold M, one associates its singular support SS(F), a closed conic co-isotropic subset of the cotangent bundle T*M, similarly as one associates its characteristic variety char(M) to a coherent D-module M on a complex manifold X.
In this talk, I will explain the notion of microsupport of sheaves (with many examples), describe its functorial properties and give some applica­tions to linear PDE and also, if times allows it, to symplectic topology.

References
  • [1] M. Kashiwara and P. Schapira, Sheaves on Manifolds, Grundlehren der Math. Wiss. 292 Springer-Verlag (1990).
  • [2] P. Schapira, Triangulated categories for the analysts, in ”Triangulated categories” London Math. Soc. LNS 375 Cambridge University Press, pp 371-389 (2010)
10/29/12

Two extra seminars on D-modules

There will be two extra seminars in week 29.10. - 2.11. on D-modules which will briefly repeat what we did last semester.

  • V. Tucek: Bundle D_X and it's submodules. Tuesday, 30.10., 14:00-15.30, K11
  • L. Krizka: Coherent and holonomic D_X-modules. Thursday, 1.11., 12.40-13.55, seminar room of Department of Algebra
10/10/12

ECI Workshop in Třešť 19.-20.10.



Programme:

Friday:

Plenary lectures

11.00 – 11.50 Tomas Tyc Waves in perfect lenses
12.30 – 14.00 Lunch
14.00 – 14.50 Jan Trlifaj Approximations and locally free modules
15.00 – 15.50 Dany Majard N-tuple groups and the Poincaré group
15.50 – 16.15 Coffee break
16.15 – 17.05 Michal Marvan Constant astigmatism equation
17.10 – 18.00 Branislav Jurco
18.00 – 19.00 Dinner
20.00 – ?? Party & Discussions

Saturday:

Algebra section

09.00 – 09.30 Michael Makkai Semistrict higher categories
09.30 – 10.00 Pavel Prihoda
10.00 – 10.30 Michael Lieberman Categories in abstract model theory
10.30 – 11.00 Coffee break
11.00 – 11.30 John Bourke Exactness properties of 2-categories
11.30 – 12.00 Jiri Rosicky Are weak equivalences finitely accessible?
12.00 – 13.30 Lunch

Geometry and Physics section

Announced lectures:

Dalibor Smid Higher order higher spin confomally invariant operators on the sphere
Ioannis Chrysikos Einstein metrics on flag manifolds with second Betti number b2(M)=1
Hong Van Le Bulk deformation of coisotropic submanifolds
Alexander Medvedev Conformal geodesics and geometry of the 3rd order ODEs systems


More info at AMeGa webpage.
9/19/12

Three Guests in Autumn

  • Pierre Schapira - Algebraic microlocal analysis

    Schapira works in algebraic analysis, especially in Sato microlocal analysis, which he combined with concepts of the French analyst school (Jean Leray, Alexander Grothendieck). He worked closely with Kashiwara, whom he met in 1971 in Japan, which was then 1976/77 in Paris, and with which he has published several books. Schapira is now a profesor at Université Paris VI.

    Three lectures on the topic: PDF.
  • Roger and Sylvia Wiegand

    Both work in commutative algebra at University of Nebraska. Topics will be announced later but Sylvia will probably speak about tame-wild dichotomy for commutative noetherian rings.
Precise dates of all lectures will be announced later.
9/17/12

Jan Šťovíček honored by ICRA 2012 Award

We are happy to announce a great success that last week in Bielefeld reached the one of the young key members of the Prague branch of ECI Jan Šťovíček. At the ICRA conference, attended by nearly 300 mathematicians and competition from other candidates, Jan became the laureate of the ICRA Award for young talent in the theory of representations.



For more info see http://www.math.uni-bielefeld.de/icra2012/icraaward.php.
6/27/12

ECI COLLOQUIUM



Thursday, June 28, 2pm, room K3



Gena Puninski

(Belarus State University, Minsk)



Pure injective modules over string algebras



Classic works of Gelfand-Ponomarev and Butler- Ringel have described all finite dimensional representations of string algebras.


Attempts at extending the classification to pure-injective representations have led Ringel to formulate a conjecture in the domestic case, saying that the indecomposable pure injective representations are completely determined by two kinds of combinatorial data, called bands and strings.


Puninski has recently proved this conjecture in the 1-domestic case. In the ECI Colloquium talk, he will present a general introduction to representation theory of string algebras as well as the main ideas of his proof of Ringel’s conjecture.

6/21/12
Two special algebra seminars
  • Monday 25.6. from 15:30: Greg Stevenson (Univ. Bielefeld) Classification problems for triangulated categories.

  • Wednesday 27.6. from 16:00: Ivo Dell'Ambrogio (Univ. Bielefeld) A homotopical look at classical Morita theory.
    Abstract: Quite recently, Gonçalo Tabuada and I have noticed a rather amusing little fact: there is a very nice Quillen model structure on the category of small preadditive categories, such that two rings become isomorphic in its homotopy category if and only if they are Morita equivalent, in the usual sense. Even better, we can use this to provide conceptual links on Morita equivalence, Picard groups, the Grothendieck group and (working relative to a base commutative ring) the notion of Azumaya algebra.
5/17/12
ECI WORKSHOP ON CATEGORIES, ALGEBRAS AND REPRESENTATIONS

See http://eci.karlin.mff.cuni.cz/events/,,, for more details.
4/18/12


Call for a position commencing in 2012



The Eduard Čech center had been established in 2005 and, since 2012, it continues as the national research center focusing its attention to interactions between algebra, geometry, and mathematical physics. The participating institutions are Faculty of Science of Masaryk University in Brno, Faculty of Mathematics and Physics of the Charles University in Prague, Institute of Physics of the Academy of Sciences of the Czech Republic and the Mathematics Institute of the Silesian University in Opava (see http://eci.sci.muni.cz).



The Center invites applications for several research positions commencing during the academic year 2012/2013 at the date depending on mutual agreement. The positions are initially for one year with a possibility of extension. The candidates must be recent PhD's and should submit a letter of application accompanied by a CV, list of publications and an outline of their research project to Professor Jiri Rosicky (rosicky@math.muni.cz) not later than


May 15, 2012.



They should also arrange for at least 2 letters of recommendation (one can be from a Czech mathematician) to be mailed directly to rosicky@math.muni.cz before May 15, 2012. The successful applicants will be notified as soon as possible but not later than June 30, 2012.





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