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 - 10.30
Coffee break
10.30 - 11.30
Šťovíček, Generalized Hill lemma
11.30 - 12.00
Trlifaj (Co)tilting, (co)filtrations, and (co)localization."
12.00 - 13.00
Lunch
13.00 - 13.30
Rosický, Shelah's singular compactness theorem
13.30 - 14.00
Raventos, Stabilization of quasicategories
14.00 - 14.30
Bourke, TBA
14.30 - 15.00
Coffee break
15.00 - 18.00
Discussion
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.
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)
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
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
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.
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.
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
b_{2}(M)=1
Hong Van Le
Bulk deformation of coisotropic submanifolds
Alexander Medvedev
Conformal geodesics and geometry of the 3rd order ODEs systems
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.
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.
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
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.