Cirriculum Vitæ

Download pdf »

 

Luke Williams

Department of Mathematics       Cell Phone: (xxx) xxx-xxxx
Michigan State University       Office Phone: (517) 355-5279
C120 Wells Hall      
East Lansing, MI 48824 - 1027       will2086@math.msu.edu    

Research Interests
Low-dimensional topology: smooth 4-manifolds, handlebody theory, Stein domains, symplectic and contact geometry, exotic structures, knot theory.

Education  

  • Ph.D., Mathematics, Michigan State University, 2015 expected.
    Advisor: Selman Akbulut
  • M.S., Mathematics, University of Nevada, Reno, 2008.
    Advisor: Stanislav Jabuka
    Thesis: Obstructing Sliceness in a Family of Montesinos Knots
  • B.S. with High Distinction, Mathematics, University of Nevada, Reno, 2006.
    Minor: Geology

 

Preprints  

  • On Handlebody Structures of Rational Balls, arXiv e-prints (2014), 1406.1575.
  • Obstructing Sliceness in a Family of Montesinos Knots, arXiv e-prints (2008), 0809.1247.

 

Awards & Honors  

  • Dissertation Completion Fellowship - Michigan State University (2015).
  • Senior Graduate Teaching Assistant Award for Excellence in Teaching - Michigan State University (2013).
  • Junior Graduate Teaching Assistant Award for Excellence in Teaching - Honorable Mention, Michigan State University (2010).
  • College of Natural Science Summer Support Fellowship - Michigan State University (2008).
  • Excellence in Scholarship Award - Mathematics and Statistics, University of Nevada, Reno (2008).
  • Jerry and Betty Wilson Scholarship, University of Nevada, Reno (2006-7 & 2007-8)
  • Millennium Scholarship, University of Nevada, Reno (2001-2006)

 

Invited Talks  

  • “On Handlebody Structures of Rational Balls” - November 20, 2014 - Geometry and Topology Semniar - University of Pennsylvania.
  • “On Handlebody Structures of Rational Balls” - October 6, 2014 - Topology Semincar - University of Texas at Austin.
  • “On Handlebody Structures of Rational Balls” - August 22, 2014 - Graduate Workshop on 4-Manifolds - Simons Center for Geometry and Physics.
  • “Stein Structures on Contractible 4-Manifolds” - January 12, 2013 - AMS Special Session on Knots, Links, and Three-manifolds - 2013 Joint Mathematics Meetings.

 

Workshops & Conferences Attended  

  • Workshop on 4-Manifolds
    Simons Center for Geometry and Physics, Stony Brook, NY (August 18-22, 2014).
  • Third Annual Tech Topology Conference
    Georgia Institute of Technology, Atlanta, GA (December 6-8, 2013).
  • Workshop and Conference on the Topology and Invariants of Smooth 4-Manifolds
    University of Minnesota, Minneapolis, MN (July 31 - August 10, 2013).
  • 2013 Join Mathematics Meetings
    San Diego Convention Center, San Diego, CA (January 9-12, 2013).
  • Midwest Topology Seminar
    Michigan State University, East Lansing, MI (October 27-28, 2012).
  • Workshop and Conference on Holomorphic Curves and Low Dimensional Topology
    Stanford University, Palo Alto, CA (July 30 - August 11, 2012).
  • Ninth Annual Graduate Student Topology and Geometry Conference
    Michigan State University, East Lansing, MI (April 2-3, 2011).
  • Eleventh Chico Topology Conference & Fortieth Cascade Topology Seminar
    Chico State University, Chico, CA (May 9-11, 2008).

 

Teaching Experience  

  • Michigan State University
    • Lecturer, MTH 202 Elementary Mathematics for Teachers II - (Fall 2014).
    • Supervisor, Lead Teaching Assistant for first Summer Session - (Summer 2014, Summer 2013, Summer 2012).
    • Lecturer, MTH 132 Calculus I - (Spring 2014, Fall 2013)
    • Recitation Leader, MTH 317H Honors Linear Algebra - (Spring 2013).
    • Teaching Assistant, MTH 868 Geometry and Topology I - (Fall 2012).
    • Lecturer, MTH 124 Survey of Calculus I - (Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009, Spring 2009).
    • Supervisor, Mathematics Learning Center - (Spring 2011, Fall 2010).
    • Lecturer, MTH 1825 Intermediate Algebra - (Summer 2009).
    • Lecturer, MTH 103 College Algebra - (Fall 2008).
  • University of Nevada, Reno
    • Recitation Leader, Math 182 Calculus II - (Spring 2008, Spring 2007).
    • Lecturer, Math 127 Precalculus II - (Fall 2007).
    • Lecturer, Math 126 Precalculus I - (Fall 2006).

 

Departmental & Submitted Talks  

  • “On Handlebody Structures of Rational Balls” - September 22, 2014 - Topology Semniar - Michigan State University.
  • Gompf, Scharlemann, and Thompson’s “On the Generalized Property R and Slice-Ribbon Conjectures” - October 19, 2011 - Topology Seminar - Michigan State University.
  • “Obstructing Sliceness in a Family of Montesinos Knots” - February 18, 2009 - 3- & 4- Manifolds Seminar - Michigan State University.
  • “Obstructing Sliceness in a Family of Montesinos Knots” - May 10, 2008 - Eleventh Chico Topology Conference & Fortieth Cascade Topology Seminar - Chico State University.
  • Graduate Student Geometry / Topology Seminars - Michigan State University:
    • “Exotic ℝ4’s” - November 26, 2013.
    • “The h-principle” - March 13, 2013.
    • “Principal Bundles” - November 1, 2012.
    • “Generalized nuclei and exotic structures” - February 16, 2012.
    • “Handlebodies and the Andrews-Curtis conjecture” - November 1, 2011.
    • “On the Heegaard Floer homology of plumbed 3-manifolds” - April 7, 2011.
    • “Some basics of symplectic topology and Kähler manifolds” - October 28, 2010.
    • “Knot colorability and knot groups” - March 19, 2010.
    • “Branched Covers” - October 29, 2009.
    • “Obstructing Sliceness in a Family of Montesinos Knots” - February 13, 2009.

 

Professional Membership   

  • American Mathematical Society (2008 - present).