I am interested in lowdimensional topology and, in particular, interactions between 3dimensional and 4dimension manifolds, constructions of exotic 4manifolds, and knot theory.
Recently, I have been exploring which negative definite plumbings of disk bundles over the 2sphere with associated graphs containing exactly one cycle have boundaries that also bound rational homology circles. Such plumbings can be used to construct rational homology 3spheres that bound rational homology 4balls as well as exotic 4manifolds via cutandpaste.
In a related direction, I have also been exploring socalled χslice links, which are links in the 3sphere that bound properly and smoothly embedded surfaces with no closed components and Euler characteristic 1 in the 4ball. One motivation behind studying such links is that the double covers of the 3sphere branched along χslice links with nonzero determinant are rational homology 3spheres that bound rational homology 4balls.

Geography of symplectic Lefschetz fibrations and rational blowdowns.
Abstract
We produce simply connected, minimal, symplectic Lefschetz fibrations realizing all the lattice points in the symplectic geography plane below the Noether line. This provides a symplectic extension of the classical works populating the complex geography plane with holomorphic Lefschetz fibrations. Our examples are obtained by rationally blowing down Lefschetz fibrations with clustered nodal fibers, the total spaces of which are potentially new homotopy elliptic surfaces. Similarly, clustering nodal fibers on higher genera Lefschetz fibrations on standard rational surfaces, we get rational blowdown configurations that yield new constructions of small symplectic exotic 4manifolds. We present an example of a construction of a minimal symplectic exotic CP^2#5CP^2 through this procedure applied to a genus3 fibration.
with R. Inanc Baykur and Mustafa Korkmaz 
On the nonorientable 4ball genus of torus knots.
Abstract
The nonorientable 4ball genus of a knot K in the 3sphere is the minimal genus of nonorientable surfaces in the 4ball bounded by K. By amalgamating ideas from involutive knot Floer homology and unoriented knot Floer homology, we give a new lower bound on the smooth nonorientable 4ball genus of any knot. This bound is sharp for several families of torus knots, including T(4n,(2n±1)^{2}) for all positive even integers n, a family Longo showed were counterexamples to Batson's conjecture. We also prove that, whenever p is an even positive integer and p/2 is not a perfect square, then the torus knot T(p,q) does not bound a locally flat Möbius band for almost all integers q relatively prime to p.
with Fraser Binns, Sungkyung Kang, and Paula Truöl 
Classification of torus bundles that bound rational homology circles.
Abstract
In this article, we completely classify torus bundles over the circle that bound 4manifolds with the rational homology of the circle. Along the way, we classify certain integral surgeries along chain links that bound rational homology balls and explore a connection to 3braid closures whose double branched covers bound rational homology 4balls.
to appear in Algebraic and Geometric Topology 
Using rational homology circles to construct rational homology balls.
Abstract
Motivated by AkbulutLarson's construction of Brieskorn spheres bounding rational homology 4balls, we explore plumbed 3manifolds that bound rational homology circles and use them to construct infinite families of rational homology 3spheres that bound rational homology 4balls. In particular, we find infinite families of torus bundles over the circle that bound rational homology circles and provide a simple method for constructing more general plumbed 3manifolds that bound rational homology circles. We then use these rational homology circles to show that, for example, 1surgery along any twisted positivelyclasped Whitehead double of any knot bounds a rational homology 4ball and 1surgery along any unknotting number one knot K with a positive crossing that can be switched to unknot K bounds a rational homology 4ball.
Topology and its Applications, Vol. 291 (2021) 
Tight contact structures on some plumbed 3manifolds.
Abstract
In this article, we prove a generalization of a theorem of LiscaMatic to Stein cobordisms and develop a method for distinguishing certain Stein cobordisms using rotation numbers. Using these results along with standard techniques from convex surface theory and classifications of tight contact structures on certain 3manifolds due to Honda, we classify the tight contact structures on a certain class of plumbed 3manifolds that bound nonsimply connected 4manifolds. Moreover, we give descriptions of the Stein fillings of the Stein fillable contact structures.

Symplectically replacing plumbings with Euler characteristic 2 4manifolds.
Abstract
We introduce new symplectic cutandpaste operations that generalize the rational blowdown. In particular, we will define kreplaceable plumbings to be those that, heuristically, can be symplectically replaced by Euler characteristic k 4manifolds. We will then classify 2replaceable linear plumbings, construct 2replaceable plumbing trees, and use one such tree to construct a symplectic exotic ℂP^{2}#6(ℂP^{2}).
Journal of Symplectic Geometry, Vol. 18, No. 5 (2020), pp. 12851318 
Cutandpaste operations and exotic 4manifolds. 
Math Seminar Spelman College 
October 2022 
Math Club Agnes Scott College 
September 2022 
Topology Seminar University of Georgia 
April 2022 
AMS Southeastern Sectional Meeting University of Southern Alabama 
November 2021 
Research Horizons Seminar Georgia Tech 
November 2021 
Geometry Topology Working Seminar Georgia Tech 
October 2021 
AlgebraTopology Seminar University of Alabama 
October 2021 
Geometry Topology Seminar Georgia Tech 
September 2021 
Lowdimensional topology and symplectic geometry weekend Remote 
April 2021 
Geometry Seminar University of Virginia 
December 2020 
Topology Seminar Brandeis University 
October 2020 
AMS Fall Western Sectional Meeting UC Riverside 
November 2019 
Geometry and Topology Seminar University of Massachusetts Amherst 
October 2019 
Moab Topology Conference Moab, UT 
May 2019 
Symplectic Geometry, Gauge Theory, and Categorification Seminar Columbia University 
April 2019 
Geometry and Topology Seminar University of Massachusetts Amherst 
September 2018 
Geometric structures on 3 and 4manifolds InterUniversity Centre, Dubrovnik, Croatia 
June 2018 
Joint Mathematics Meetings San Diego, CA 
January 2018 
Tech Topology Conference Georgia Tech 
December 2017 
Joint Mathematics Meetings Atlanta, GA 
January 2017 
Perspectives in Topology and Geometry of 4manifolds InterUniversity Centre, Dubrovnik, Croatia 
June 2016 
AMS Southeastern Sectional Meeting University of Georgia 
March 2016 
Geometry Seminar University of Virginia 
November 2015 
A history of 4manifolds Graduate Student Seminar University of Virginia 
March 2018 
Building exotic 4manifolds Graduate Student Seminar University of Virginia 
October 2015 
Intro to Kirby Calculus Topology Student Seminar University of Virginia 
February 2015 
AMS Western Section Meetings, UC Riverside, CA  November 2019 
Knot concordance and lowdimensional manifolds, Le Croisic, France  June 2019 
Moab Topology Conference, USU Moab  May 2019 
Virginia Topology Conference, University of Virginia  December 2018 
Knotted Surfaces in 4manifolds, UMass Amherst  October 2018 
The topology and geometry of lowdimensional manifolds, UTAustin  July 2018 
Geometric Structures on 3 and 4manifolds, Dubrovnik, Croatia  June 2018 
Joint Mathematics Meetings, San Diego, CA  January 2018 
LowDimensional Topology Conference, UCLA  January 2018 
Tech Topology Conference, Georgia Tech  December 2017 
58th Annual Texas Geometry and Topology Conference, UT  Austin  November 2017 
2017 Virginia Topology Conference, University of Virginia  November 2017 
CMOBIRS: Low Dimensional Topology and Gauge Theory, Oaxaca, MX  August 2017 
Kylerec Workshop, Truckee, CA  May 2017 
Joint Mathematics Meetings, Atlanta, GA  January 2017 
Virginia Topology Conference, University of Virginia  November 2016 
Low Dimensional Topology Workshop, Central European University, Budapest, Hungary  July 2016 
Perspectives in Topology and Geometry of 4manifolds, Dubrovnik, Croatia  June 2016 
Knots in the Triangle (Knots in Washington XLII), North Carolina State University  April 2016 
Graduate Student Topology & Geometry Conference, Indiana University  April 2016 
AMS Southeastern Sectional Meeting, University of Georgia  March 2016 
Joint Mathematics Meetings, Seattle, WA  January 2016 
William Rowan Hamilton Geometry and Topology Workshop, Trinity College, Dublin, Ireland  August 2015 
Princeton Low Dimensional Topology Workshop, Princeton University  June 2015 
Redbud Topology Conference, Oklahoma State University  April 2015 
Topology Student Workshop, Georgia Tech  June 2014 
Graduate Student Topology & Geometry Conference, UT  Austin  April 2014 
Tech Topology Conference, Georgia Tech  December 2013 