TEACHING

**Fall****2017**:

Math 446: Topology

Math 808: Geometry/Topology I (Algebraic Topology)

**Spring****2017**:

Math 809: Geometry/Topology II (Differential Topology)

**Fall 2016**:

Math 216: Introduction to Abstract Math (2 sections)

**Spring****2016**:

Math 320: Introduction to Analysis

**Fall 2015**:

Math 446: Topology

Math 881: Real Analysis

**Fall 2014**:

Math 446: Topology

**Spring 2014**:

Math 211: Honors Linear Algebra

**Fall 2013**:

Math 216: Introduction to Abstract Math

Math 855: Topics in Geometry and Topology (Heegaard Floer Theory)

**Spring 2013**:

Math 216: Introduction to Abstract Math (2 sections)

**Fall 2012**:

Math 831: Geometry/Topology III (Characteristic Classes)

**Spring 2012**:

Math 210: Linear Algebra

Math 460: Complex Variables

**Fall 2011**(Princeton):

Math 217: Honors Linear Algebra

Math 981: Junior Seminar in Knot Theory

**Fall 2010**(Princeton):

Math 103: Calculus

**Spring 2009**(Princeton):

Math 203: Advanced Multivariable Calculus

Math 217: Honors Linear Algebra

**Spring 2007**(Columbia):

Calculus I

**Fall 2006**(Columbia):

Calculus I

GRADUATE ADVISING

**Kyle Hayden**,*Ph.D. Student*, 2015-

**Lev Tovstopyat-Nelip**,*Ph.D. Student*, 2014-

**Adam Saltz***, Ph.D. Student*, 2013-2016:

I advised Saltz' thesis of which one component was his paper*An annular refinement of the transverse element in Khovanov homology*with Hubbard. Saltz is now a postdoc at UGA.

UNDERGRADUATE ADVISING

**Champ Davis***, Undergraduate*, Fall 2016-:

I am advising Davis's thesis on the L-space conjecture relating Floer homology, left-orderability of the fundamental group, and taut foliations.

**Champ Davis**,**Chris Ratigan***, Undergraduates*, Summer 2016:

Davis and Ratigan worked on re-proving, using grid diagrams, a result of mine on the functoriality of the transverse braid invariant in knot Floer homology under composition of braid words.

**Sean Hamlin***, Undergraduate*, Fall 2015-Spring 2016:

I advised Hamlin's senior thesis on knot theory and DNA topology.

**Cynthia Chen, Andrew Ferdowsian, Champ Davis**,*Undergraduates*, Spring 2014-Fall 2014:

I advised Chen, Ferdowsian, and Davis as part of BC's Undergraduate Research Fellowship program. They learned knot theory basics, read research papers on Khovanov homology, and ultimately wrote a computer program to compute a certain module structure on Khovanov homology.

**Zach Miles**,*Undergraduate*, Fall 2013-Spring 2014:

I led an informal reading course for Miles on Colin Adams'*The Knot Book*.

**Daniel Kriz**,*Undergraduate*, Spring 2011-Summer 2011:

I advised Kriz as part of Princeton's summer research program. He studied the E_3 term of a twisted version of the spectral sequence from Kh(L) to HF(Σ(L)), and has written up his results (with I. Kriz) in the paper,*Baldwin-Ozsvath-Szabo cohomology is a link invariant***.**Kriz is now a math Ph.D. student at Princeton.

**Chuen Ming Mike Wong**,*Undergraduate*, Spring 2011-Winter 2011:

I advised Wong first as part of Princeton's summer research program, and then as his senior thesis advisor. He studied Manolescu's unoriented skein exact triangle in knot Floer homology (and the spectral sequence that results from iterating it) from the point of view of grid diagrams. His research resulted in the paper,*Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology*. Wong is now a math Ph.D. student at Columbia.

**Jack Sempliner**,*High School Student*, Spring 2011-Winter 2011:

I advised Sempliner during his junior and senior years in high school. His project was related to Khovanov homology and inspired by work of Seidel and Smith. He submitted his work to the Intel Science Talent Search. He is now a math Ph.D. student at Princeton.