[Contact] [Teaching] [Seminar] [Research] [Conferences] - [Schedule]

Marco Varisco

Address Department of Mathematical Sciences Binghamton University, SUNY Binghamton, NY 13902-6000 Office LN-2208A Office Hours MW 2:30-4:00 Phone 1-607-777-2903 Fax 1-607-777-2450 E-Mail marco@math.binghamton.edu URL www.math.binghamton.edu/marco/ Research Interests Algebraic and geometric topology, K- and L-theory (*) vCard

Since 2006 I am Visiting Assistant Professor at Binghamton. Until then I was in the topology group at Münster (Germany), where I finished my doctorate under the supervision of Wolfgang Lück.

Teaching

Future

Fall 2008 (Office Hours: MWF 3:30-4:30)

• Math 222: Calculus II, Section 4
  MWF 1:10-2:10 in LN-1120 and R 1:15-2:40 in LN-1120
• Math 222: Calculus II, Section 5
  MWF 2:20-3:20 in LN-1120 and T 1:15-2:40 in LN-1120
• Math 590T: Topics in Topology: Graduate Topology Seminar (with Chris Dwyer)
  R 10:15-11:15 in LN-2205

Present

Spring 2008 (Office Hours: MW 2:30-4:00)

• Math 601A: Topics in Topology: Algebraic K-Theory
  MW 4:00-5:30 in LN-2205
• Math 590T: Topics in Topology: Graduate Topology Seminar (with Chris Dwyer)
  R 10:15-11:15 in LN-2205

Past

Fall 2007 (Office Hours: MWF 1:10-2:10)

• Math 221: Calculus I, Section 12
  MWF 12:00-1:00 in LN-G335 and R 11:40-1:05 in LN-G85
• Math 221: Calculus I, Section 21
  MWF 2:20-3:20 in S2-337 and R 1:15-2:40 in LN-G335
• Math 590T: Topics in Topology: Graduate Topology Seminar (with Chris Dwyer)
  R 10:15-11:15 in LN-2206

Spring 2007 (Office Hours: MW 3:00-4:30)

• Math 601A: Topics in Topology: Lie Groups
  MW 4:40-6:15 in LN-2205
• Math 590T: Topics in Topology: Graduate Topology Seminar (with Chris Dwyer)
  TR 10:15-11:15 in LN-2205

Fall 2006 (Office Hours: W 2:30-4:00 and R 10:00-11:30)

• Math 221: Calculus I, Section 21
  MWF 12:00-1:00 in SW-321 and R 8:30-9:55 in SW-325
• Math 221: Calculus I, Section 23
  MWF 1:10-2:10 in AP-G15 and T 2:50-4:15 in FA-209

Geometry and Topology Seminar

Thursdays 2:50-3:50 in LN-2205 [Home] [Google Calendar] [iCal] [xml]

Research

• Algebraic K-theory of group rings and topological cyclic homology.
  Wolfgang Lück, Holger Reich, John Rognes, and Marco Varisco.
  In preparation.
  

  Abstract: We use topological cyclic homology and the cyclotomic trace to detect elements in the rationalized higher algebraic K-theory groups of integral group rings. Modulo a deep conjecture in number theory, the so-called Schneider conjecture, and under mild homological finiteness conditions on the group, we prove that the connective algebraic K-theory assembly map for the family of virtually cyclic subgroups is rationally injective. This generalizes a result of Bökstedt, Hsiang, and Madsen, and leads to a concrete description of a large direct summand inside the algebraic K-theory groups of an integral group ring in terms of group homology. Along the way we also prove integral splitting and isomorphism results for THH- and TC-assembly maps with coefficients in arbitrary connective ring spectra.

• Commuting homotopy limits and smash products.
  Wolfgang Lück, Holger Reich, and Marco Varisco.
  K-Theory, 30(2):137-165, 2003.
  [arXiv:math/0302116] [pdf] [djvu] [ps] [MR2064237]

  Abstract: In general the processes of taking a homotopy inverse limit of a diagram of spectra and smashing spectra with a fixed space do not commute. In this paper we investigate under what additional assumptions these two processes do commute. In fact we deal with an equivariant generalization which involves spectra and smash products over the orbit category of a discrete group. Such a situation naturally occurs if one studies the equivariant homology theory associated to topological cyclic homology. The main theorem of this paper will play a role in the generalization of the results obtained by Bökstedt, Hsiang and Madsen about the algebraic K-theory Novikov Conjecture to the assembly map for the family of virtually cyclic subgroups.

• Algebraic L-theory and triangular Witt groups.
  Ph.D. thesis, Münster.

  Abstract: The classical Witt groups of quadratic forms have been generalized in algebraic topology, with Wall's and Ranicki's L-groups for surgery theory, and in algebraic geometry, with Knebusch's Witt groups of schemes and Balmer's Witt groups of triangulated categories with duality.
  We introduce algebraic L-theory groups for so-called pre-triangulated differential graded categories with duality, generalizing and unifying the two aforementioned approaches.

Conferences

Travel Plans

• Surgery and Manifold Theory. Andrew Ranicki's 60th birthday conference.
  Münster University (Germany), June 19 to 20, 2008.
• Third Arolla Conference on Algebraic Topology.
  Hôtel du Mont-Collon, Arolla (Switzerland), August 18 to 24, 2008.

Past

• Special Session on Geometric Topology at the AMS 2008 Spring Eastern Meeting.
  Courant Institute of Mathematical Sciences, New York University, March 15 to 16, 2008.
• Singularities in Geometry and Topology. In honor of Sylvain Cappell's 60th birthday.
  Courant Institute of Mathematical Sciences, New York University, March 17 to 20, 2008.
• Visiting the University of Chicago, and talk in the Geometry/Topology Seminar.
  University of Chicago (IL), November 14 to 18, 2007.
• Visiting Penn State Altoona, and talk in the Topology/Geometry Seminar.
  Penn State Altoona (PA), October 18 to 20, 2007.
• Cohomology of Groups and Algebraic K-Theory.
  CMS, Zhejiang University, Hangzhou (China), July 2 to 12, 2007.

Older

• Visiting the Sonderforschungsbereich "Geometrische Strukturen in der Mathematik".
  Münster University (Germany), June 1 to 30, 2007.
• Topology Festival.
  Cornell University, Ithaca (NY), May 21 to 24, 2007.
• Talk at the Topology & Geometric Group Theory Seminar.
  Cornell University, Ithaca (NY), April 24, 2007.
• Nil Phenomena in Topology.
  Vanderbilt University, Nashville (TN), April 14 to 15, 2007.
• Visiting Miami of Ohio, and talk in the Topology Seminar.
  Miami University, Oxford (OH), March 31 to April 9, 2007.
• AMS 2007 Spring Central Section Meeting.
  Miami University, Oxford (OH), March 16 to 17, 2007.
• Topology Workshop.
  BIRS, Banff (Canada), February 25 to March 2, 2007.
• Winter 2007 Midwest Topology Seminar.
  University of Illinois at Chicago, February 24, 2007.
• Geometry, Topology, and their Interactions. An international conference in honor of Farrell-Jones.
  Morelia (Mexico), January 8 to 13, 2007.
• Frank Quinn's 60th Birthday Conference.
  Binghamton University, SUNY, November 5 to 7, 2006.
• Surgery Theory Past, Present and Future. A celebration of the 70th birthday of C.T.C. Wall.
  ICMS, Edinburgh (UK), July 3 to 5, 2006.
• Prospects in Topology. A celebration of the 60th birthdays of Ian Hambleton and Erik Kjær Pedersen.
  Münster University (Germany), June 28 to 29, 2006.

Conferences and Seminars Organized

• Special Session on Geometric Topology at the AMS 2008 Spring Eastern Meeting (with David Rosenthal).
  Courant Institute of Mathematical Sciences, New York University, March 15 to 16, 2008.
• Geometry and Topology Seminar.
  Binghamton University, Fall Semester 2007 and Spring Semester 2008.
• Workshop on Trace Methods in Algebraic K-Theory (with Lars Hesselholt, Wolfgang Lück, and Holger Reich).
  Münster University (Germany), September 29 to October 3, 2003.
• Seminar on trace maps (with Holger Reich).
  Münster University (Germany), Oberseminar Topologie, Sommersemester 2001 & Wintersemester 2001/2002.
• Fragestunde/Kleines Seminar & Rothenberge Workshops.
  Münster University (Germany), GK/SFB, 2001 to 2004.

What is Topology, anyway?

Here is Robert Bruner's “short and idiosyncratic” answer.

Marco Varisco - April 4, 2008.