## Homological Methods Seminar

The Homological Methods Seminar will meet Wednesday mornings from 10 to 12 in HU 1018, for talks on the use of homological methods in Algebra, Algebraic Geometry, and Representation Theory.

Aside from invited outside visitors, we are particularly interested in talks by local graduate students and postdocs who wish to present their results.

This year we will set aside the first hour as a Learning Seminar. The topic will be "Free Divisors", as they appear in singularity and deformation theory, group actions, quiver representations, hyperplane arrangements, and other situations.

For the organizational meeting, see below. If you would like to suggest a speaker, including yourself, please contact Ragnar-Olaf Buchweitz or Brian Pike

### The singular Milnor number of matrix singularities

by Brian Pike | University of Toronto Scarborough
Time: 10:10  (Wednesday, Nov. 23, 2011)
Location: HU1018, 215 Huron St
Abstract:
For isolated hypersurface and isolated complete intersection singularities, the Milnor number is an invariant of the singularity which describes the topology of an associated topological space. Damon and Mond found a generalization, the \emph{singular Milnor number}, which is defined quite generally for even nonisolated singularities. The main case where a formula for the singular Milnor number exists involves singularities formed from free divisors; in this talk, I will show how this is enough to compute the singular Milnor number for certain matrix singularities which are not free divisors.

#### Dates in this series

· Wednesday, Sep. 29, 2010: Tilting Bundles on Rational Surfaces and Quasi-Hereditary Algebras (Lutz Hille)
· Wednesday, Oct. 06, 2010: On Picard-Fuchs-Equations of invertible polynomials (Swantje Gährs)
· Wednesday, Oct. 13, 2010: Complete Resolutions over Complete Intersections, Part I (Ragnar-Olaf Buchweitz)
· Wednesday, Oct. 20, 2010: Poisson modules on projective varieties (Brent Pym)
· Wednesday, Oct. 27, 2010: Hilbert Depth (Thuy Pham)
· Wednesday, Nov. 10, 2010: On the decomposability of maximally Cohen-Macaulay modules over hypersurface singularities (Dmitry Kerner)
· Wednesday, Nov. 17, 2010: Complete Resolutions over Complete Intersections, Part II (Ragnar-Olaf Buchweitz)
· Wednesday, Nov. 24, 2010: Complete Resolutions over Complete Intersections, Part III (Ragnar-Olaf Buchweitz)
· Wednesday, Dec. 01, 2010: Smooth double subvarieties in singular varieties (M. R. Gonzalez-Dorrego)
· Wednesday, Jan. 19, 2011: Organizational meeting (Ragnar-Olaf Buchweitz)
· Wednesday, Jan. 26, 2011: Organizational Meeting, Part II (Ragnar-Olaf Buchweitz)
· Wednesday, Feb. 09, 2011: Asymptotic behavior of the dimension of syzygy modules (Micah Leamer)
· Wednesday, Feb. 16, 2011: Foliations bu curves in the projective plane (Jorge Olivares)
· Wednesday, Mar. 09, 2011: What do we know about matrix factorizations? (Ragnar-Olaf Buchweitz)
· Wednesday, Mar. 16, 2011: Wild Hypersurfaces (Graham Leuschke)
· Wednesday, Mar. 23, 2011: The Existence of Totally Reflexive Modules via Gorenstein Homomorphisms (Kristen A. Beck)
· Wednesday, Sep. 14, 2011: Organizational Meeting and Survey on Free Divisors (Ragnar-Olaf Buchweitz)
· Wednesday, Sep. 21, 2011: Normal crossing divisors and their singularities (Eleonore Faber)
· Wednesday, Sep. 21, 2011: Free Divisors: Discriminants in Versal Deformations of Isolated Complete Intersection Singularities (Ragnar-Olaf Buchweitz)
· Thursday, Sep. 22, 2011: Visualizing singularities (Eleonore Faber)
· Monday, Sep. 26, 2011: Universal extensions, tilting bundles, Markov type equations and algebras defined by polygons (Lutz Hille)
· Wednesday, Sep. 28, 2011: Free Divisors: Discriminants in Versal Deformations of Isolated Complete Intersection Singularities II (Ragnar-Olaf Buchweitz)
· Wednesday, Oct. 05, 2011: An Introduction to Linear Free Divisors (Brian Pike)
· Wednesday, Oct. 12, 2011: An Introduction to Linear Free Divisors II (Brian Pike)
· Wednesday, Oct. 19, 2011: An Introduction to Linear Free Divisors III (Brian Pike)
· Wednesday, Oct. 26, 2011: Free hyperplane arrangements (Brent Pym)
· Wednesday, Nov. 02, 2011: Free Divisors Arising from Reflection Groups (Collin Roberts)
· Wednesday, Nov. 09, 2011: Free divisors arising as deformations of curve singularities (Mikhail Gudim)
· Wednesday, Nov. 16, 2011: On the discriminant of space curve singularities (Dmitry Kerner)
· Wednesday, Nov. 23, 2011: The singular Milnor number of matrix singularities (Brian Pike)
· Wednesday, Nov. 30, 2011: Introduction to the representation of quivers (Louis-Philippe Thibault)
· Wednesday, Dec. 07, 2011: On the discriminant of space curve singularities II (Dmitry Kerner)
· Wednesday, Jan. 18, 2012: Linear Free Divisors from Quiver Representations (Ragnar-Olaf Buchweitz)
· Wednesday, Jan. 25, 2012: Linear free divisors from block representations (Brian Pike)
· Tuesday, Jan. 31, 2012: D-modules and coinvariants of Lie algebras of vector fields (Travis Schedler)
· Wednesday, Feb. 01, 2012: An algebraic extension of the L\^e-Saito Theorem (Mathias Schulze)
· Wednesday, Feb. 08, 2012: Classification of weighted homogeneous Saito free divisors in $C^3$ (Louis-Philippe Thibault)
· Wednesday, Feb. 15, 2012: Free divisors over other rings (Mikhail Gudim)
· Wednesday, Feb. 29, 2012: Free Hyperplane Arrangements and the $K(\pi,1)$ Question (Kevin Luk)
· Wednesday, Mar. 07, 2012: An adaptation of Schwede's loop bracket construction for monoidal categories (Reiner Hermann)
· Wednesday, Mar. 14, 2012: F-manifolds and free divisors I (Sasha Pavlov)
· Wednesday, Mar. 21, 2012: F-manifolds and free divisors II (Sasha Pavlov)
· Wednesday, Mar. 28, 2012: On The Freeness of 3-Arrangements (Ali Mousavidehshikh)
· Wednesday, Apr. 04, 2012: F-manifolds and free divisors III (Sasha Pavlov)
· Tuesday, Sep. 11, 2012: From Platonic Solids to Cluster Categories --- A Journey into Noncommutative Projective Geometry (Ragnar-Olaf Buchweitz)
· Wednesday, Sep. 12, 2012: Bicategories and Matrix Factorizations (Brian Pike)
· Wednesday, Sep. 19, 2012: Matrix factorizations, maximal Cohen-Macaulay modules and the triangulated category of singularities (Eleonore Faber)
· Wednesday, Oct. 03, 2012: Knorrer periodicity (Louis-Philippe Thibault)
· Wednesday, Oct. 10, 2012: Maximal Cohen-Macaulay modules of Kleinian singularities (Brian Pike)
· Wednesday, Oct. 24, 2012: Homological Properties of the singularity category (Chris Dodd)
· Wednesday, Oct. 31, 2012: Homological Properties of the singularity category II (Chris Dodd)
· Wednesday, Nov. 07, 2012: Almost split triangles versus Serre duality (Ragnar-Olaf Buchweitz)
· Wednesday, Nov. 14, 2012: Orlov's Theorem (Chris Dodd)
· Wednesday, Nov. 21, 2012: The Fourier-Mukai transform (Mikhail Gudim)
· Wednesday, Nov. 28, 2012: Weighted projective spaces (Ali Mousavidehshikh)
· Wednesday, Dec. 05, 2012: Hochschild homology, intersection pairing and Hirzebruch-Riemann-Roch formula (Sasha Pavlov)
· Wednesday, Dec. 12, 2012: Matrix factorizations and Landau-Ginzburg models (Brent Pym)
· Wednesday, Dec. 12, 2012: Cluster categories associated to new hereditary categories (Adam-Christiaan van Roosmalen)
· Tuesday, Jan. 22, 2013: Morita Contexts (Mikhail Gudim)
· Tuesday, Feb. 05, 2013: Derived Morita Theory (Brian Pike)