Zakład Algebry i Geometrii Algebraicznej
The Department of Algebra and Algebraic Geometry was founded in 2000.
It is, in some sense, a continuation of the IM PAN Department of Algebra
in Toruń, directed at first by Jerzy Łoś and then by Stanisław Balcerzyk.
For the history of the latter, see the summary by S. Balcerzyk published
in the booklet edited on the occasion of the 50th anniversary of IM PAN,
The following mathematicians have worked in the Department of Algebra
and Algebraic Geometry in the period 2000–2008: Janusz Adamus, Marcin
Chałupnik, Sławomir Cynk, Piotr Hajac, Joanna Jaszuńska, Zbigniew Jelonek,
Paweł Kasprzak, Jarosław Kędra, Oskar Kędzierski, Mariusz Koras, Urlich
Kraehmer, Adrian Langer, Tomasz Maszczyk, Jerzy Płonka, Piotr Pragacz (head),
Agata Smoktunowicz, Tomasz Szemberg, Marek Szyjewski, Halszka Tutaj-Gasińska,
Bronisław Wajnryb, Andrzej Weber, and Bartosz Zieliński.
The spectrum of the interest of mathematicians in the department is marked
by the following topics (displayed in alphabetical order):
- Affine algebraic geometry (Jelonek)
- Algebraic topology (Chałupnik, Weber)
- Classical algebra and combinatorics (Pragacz)
- Complex projective algebraic geometry (Cynk, Kedzierski, Langer,
Pragacz, Tutaj-Gasińska, Szemberg)
- Enumerative theory of singularities (Pragacz, Weber)
- Geometry and topology of surfaces (Wajnryb)
- K-theory (Szyjewski)
- Moduli spaces (Langer)
- Noncommutative geometry and quantum groups (Hajac, Kasprzak,
Kraehmer, Maszczyk, Zieliński)
- Noncommutative rings (Smoktunowicz)
- Symplectic geometry and topology (Kędra)
- Universal algebra (Płonka)
The "center" of mathematical life of the department is the
Its leading subject is complex algebraic geometry. The seminar meets
each two weeks (for two sessions with a break for discussions), and gather
algebraic geometers from all around of Poland. The
seminar IMPANGA hosted
as speakers: F. Hirzebruch, H. Esnault, G. van der Geer, J. Kollar
and many others.
IMPANGA also organizes at the Banach Center mini-schools, directed
especially towards young researchers from all around of Europe.
Let us mention here, e.g., the following mini-schools of IMPANGA :
"Characteristic classes" (2002), "Schubert varieties" (2003),
and "Moduli spaces" (2005). In 2003, IMPANGA organized jointly with
Institutes of Mathematics of Bulgarian, Hungarian and Romanian Academy
of Sciences, the Conference and Summer School "Algebraic Geometry,
Algebra, and Applications" in Borovetz (Bulgaria). Two sessions, prepared
by IMPANGA at the Banach Center for a wider audience (from history and
philosophy of sciences), were devoted to Grothendieck (2004) and
Hoene-Wroński (2007). Consult the above web-page for the list of IMPANGA
events and details of these activities.
The outgrowth of seminars and schools of IMPANGA was published in
Topics in cohomological studies of algebraic varieties (2005),
Algebraic cycles, sheaves, shtukas, and moduli (2007),
edited by Birkhauser-Verlag,
Hoene-Wroński: Życie, Matematyka i Filozofia (2008), edited by IM PAN.
The seminar IMPANGA
also stimulated research of mathematicians
not working directly in the department. Let us mention here, e.g.,
the papers: "A cascade of determinantal Calabi-Yau threefolds" by
M. and G. Kapustka from the Jagiellonian University (math.AG/08023669),
and "On Thom polynomials for A4(-) via Schur functions" by O. Ozturk
from METU in Ankara (Serdica Math. J. 33 (2007), 301-320).
Another very active seminar in the department, organized by P. Hajac
and T. Maszczyk, was
"Noncommutative geometry and quantum groups".
For the content of this seminar (among the speakers were the Fields
medalists: A. Connes and M. Kontsevich), and for many related
activities on noncommutative geometry at IM PAN, including the
Conference in honor of Paul Baum's 70th Birthday (2007), see
of mathematicians from the department
- J. Adamus, E. Bierstone and P.D. Milman, Uniform linear bound in
Chevalley's lemma, to appear in Canad. J. Math. (2008),
- T. Bauer, T. Szemberg, Local positivity of principally polarized
abelian threefolds, J. Reine Angew. Math. 531 (2001) 191-200,
- P.F. Baum, P.M. Hajac, R. Matthes and W. Szymański, The K-theory of
Heegaard-type quantum 3-spheres, K-Theory 35 (2005), 159-186.
- P.F. Baum, P.M. Hajac, R. Matthes and W. Szymański, a chapter in the
forthcoming volume "Quantum Symmetry in Noncommutative Geometry",
European Mathematical Society Publishing House.
- B. Bojarski, A. Weber, Generalized Riemann-Hilbert transmission and
boundary value problems, Fredholm pairs and bordisms, Bull. Polish
Acad. Sci. Math. 50 (2002), 479-496.
- P. Cassou-Nogues, M. Koras and P. Russell, Smooth embeddings of C*
into C2, part I., to appear in J. Algebra (2008)
- S. Cynk, Defect of a nodal hypersurface, Manuscripta Math. 104
- T. Hadfield, U. Kraehmer, Twisted Homology of Quantum SL(2), K-Theory
34 (2005), 327-360.
- P.M. Hajac, R. Matthes and W. Szymański, A locally trivial quantum
Hopf fibration, Algebr. Represent. Theory 9 (2006), 121-146.
- S. Janeczko, Z. Jelonek, Linear automorphisms that are symplectomorphisms,
J. of the London Math. Soc. 69 (2004), 503-517.
- Z. Jelonek, The Łojasiewicz exponent and effective Nullstellensatz,
- Z. Jelonek, K. Kurdyka, On asymptotical critical values of a complex
polynomial, J. Reine Angew. Math. 565 (2001), 1-11.
- J. Kędra, D. McDuff, Homotopy properties od Hamiltonian group
actions, Geometry and Topology, vol.9 (2005), Paper no.3, pp. 121-162.
- A. Langer, Semistable principal G-bundles in positive characteristic,
Duke Math. J. 128 (2005), 511-540.
- A. Langer, Moduli spaces and Castelnuovo-Mumford regularity of sheaves
on surfaces, Amer. J. of Math. 128 (2006), 373-417.
- A. Langer, T. Gomez, A. Schmitt, I. Sols, Moduli spaces for principal
bundles in arbitrary characteristic, preprint (2006).
- A. Lascoux, P. Pragacz, Double Sylvester sums for subresultants and
multi-Schur functions, J. Symb. Comp. 35 (2003), 689-710.
- T.H. Lenagan, A. Smoktunowicz, An infinite dimensional affine nil
algebra with finite Gelfand-Kirillov dimension, Journal of the A.M.S.
20 (2007), 989-1001.
- T. Maszczyk, A pairing between super Lie-Rinehart and periodic cyclic
homology, Comm. in Math. Physics, 263 (2006), 737-747.
- T. Maszczyk, One-dimensional infinitesimal-birational duality through
differential operators, Fund. Math. 191 (2006), 23-43.
- A. Parusiński, P. Pragacz, Characteristic classes of hypersurfaces
and characteristic cycles, J. Alg. Geom. 10 (2001), 63-79.
- J. Płonka, Subvarieties of the clone extension of the variety
of distributive lattices, Algebra Universalis 55 (2006), 175-186.
- P. Pragacz, Multiplying Schubert classes, in "Topics in cohomological
studies of algebraic varieties", Trends in Math., Birkhauser (2005),
- P. Pragacz, Thom polynomials and Schur functions: the singularities
I22(-), Annales de l'Institut Fourier 57 (2007), 1487-1508.
- P. Pragacz, V. Srinivas and V. Pati, Diagonal subschemes and vector
bundles, math.AG/0609381 - to appear in the special volume of Quarterly
J. of Pure and Appl. Math., dedicated to J-P. Serre on his 80th Birthday
(S.T. Yau et al. eds.).
- P. Pragacz, A. Weber, Positivity of Schur function expansions of Thom
polynomials, Fund. Math. 195 (2007), 85-95.
- A. Smoktunowicz, There are no graded domains with GK dimension strictly
between 2 and 3, Inv. Math. 164 (2006), 635-640.
- A. Smoktunowicz, Some results in noncommutative ring theory, Proceedings
of the International Congress of Mathematicians, Madrid, Spain,
August 22-30, 2006, Vol 2: Invited talks, 259-269.
- A. Weber, Pure homology of algebraic varieties, Topology 43 (2004),