Alyson Lin Hildum
Hello! This is my webpage, last updated September 4, 2014.
Are you looking for someone named Alyson Burchardt? Well that's me. I'm
just married now.
About me: I'm a 2nd
year postdoctoral fellow at McMaster University in Hamilton, ON
working with Ian Hambleton. Our work together involves extending the
research of I. Hambleton, M. Kreck, and P. Teichner in classifying
geometrically 2-dimensional 4-manifolds up to s-cobordism to the case
of 4-manifolds which have fundamental group isomorphic to certain
right-angled Artin groups.
Office: Hamilton Hall 319, Department of Mathematics and Statistics,
ahildum "at" math "dot" mcmaster "dot" ca
I've been known to read/think/learn/talk about knots, braids, surgery
theory, K(G,1) spaces, Heegaard-Floer theory, Combinatorial
Heegaard-Floer theory, RAAGs, and of course, 4-manifolds.
I received my Ph.D. from Brandeis
University in May 2013, advised under Daniel Ruberman. My
dissertation research involves minimizing the Euler characteristic of a
4-manifold with specified fundamental group a right-angled Artin group,
and is summarized in my paper
on the arXiv, and soon will appear in AGT.
teaching at McMaster University:
Calculus for Engineers (Fall 2014)
at McMaster University:
- Math 1B03 Linear Algebra for Science (Spring 2013)
at Brandeis University:
- Math 1ZC3 Linear Algebra for Engineers (Spring 2013)
- MATH 10a Differential Calculus (Summer 2012)
- MATH 10b Integral Calculus (Spring 2011)
- MATH 10a Differential Calculus (Fall 2010)
- MATH 10a Differential Calculus (Spring 2010)
- MATH 5a Precalculus (Fall 2009)
- The minimum $b_2$ problem for right-angled Artin groups. 8/22/14,
Workshop on Topology and Invariants of 4-Manifolds
- The minimum $b_2$ problem for right-angled Artin groups. 3/23/13,
47th Spring Topology and Dynamics Conference
- The Hausmann-Weinberger 4-manifold invariant for right-angled
3/31/12, Indiana Graduate Student Topology Conference
talks I've given in the past:
- An introduction to knot concordance. 7/24/14, McMaster Knot
- The minimum $b_2$ problem for right-angled Artin groups.
10/31/13, McMaster Geometry/Topology Seminar
- An introduction to the classification of 4-manifolds and Kirby
4/3/12 and 4/17/12, Brandeis Topology Seminar
- On the Tristram-Levine signatures of a knot.
10/18/11, Brandeis Topology Seminar
Algebraic obstructions to concordance.
10/4/11, Brandeis Topology Seminar
- Some knots with surgeries yielding lens spaces.
4/26/10, Brandeis second-year-seminar
Abstract: John Berge wrote an unpublished paper on knots with surgeries
yielding lens spaces in which he characterizes these knots in a genus 2
Heegaard splitting of S^3. He conjectured that all knots that have
surgeries yielding lens spaces are of this characterization. He also
gives a method for finding the exact lens space resulting from surgery
of a particular knot, given that we know the homology class the knot
represents in the Heegaard splitting. I'll give some introductory
definitions/explanations on handlebody decompositions, Heegaard
splittings, 0- and 1-bridge knots, and Dehn surgery before I start to
talk about the theorems in the paper.
- An introduction to the Braid Group.
2/9/10, Brandeis Topology Seminar
- Workshop on
Topology and Invariants of 4-Manifolds, Simons Center for Geometry
and Physics, August 2014
Legacy Conference, Cornell University, June 2014
- 11th Annual
Graduate Student Topology Conference, University of Notre Dame,
Spring Topology and Dynamics Conference, Central Connecticut State
University, March 2013
- 10th Annual Graduate
Student Topology Conference, Indiana University,
Invariants in Low-Dimensional Topology, Simons
Center for Geometry and Physics, June 2011
Topology and Categorification, Stony Brook University, June 2010.