Zakład Algebry i Geometrii Algebraicznej



O Zakładzie

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, or here.

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):

  1. Affine algebraic geometry (Jelonek)
  2. Algebraic topology (Chałupnik, Weber)
  3. Classical algebra and combinatorics (Pragacz)
  4. Complex projective algebraic geometry (Cynk, Kedzierski, Langer, Pragacz, Tutaj-Gasińska, Szemberg)
  5. Enumerative theory of singularities (Pragacz, Weber)
  6. Geometry and topology of surfaces (Wajnryb)
  7. K-theory (Szyjewski)
  8. Moduli spaces (Langer)
  9. Noncommutative geometry and quantum groups (Hajac, Kasprzak, Kraehmer, Maszczyk, Zieliński)
  10. Noncommutative rings (Smoktunowicz)
  11. Symplectic geometry and topology (Kędra)
  12. Universal algebra (Płonka)

The "center" of mathematical life of the department is the seminar IMPANGA. 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 two volumes:
Topics in cohomological studies of algebraic varieties (2005),
Algebraic cycles, sheaves, shtukas, and moduli (2007), edited by Birkhauser-Verlag,
and in:
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