Email: smniemic@iu.edu

Post doctoral fellow at Indiana University interested in low dimensional topology particularly through the lens of Heegaard Floer and Knot Floer homology. Current interest is in lattice homology and in particular better understanding knot lattice homology. These tools compute an invariant for a special type of 3-manifold, a link of a normal complex surface singularity, by computing how badly the cubes of an integer lattice fails to approximate an ellipsoid. Changing the size of the ellipsoid gives a filtration on this complex, and shifting the filtration off itself then gives an invariant for a knot inside the 3-manifold. These knots are specifically generalized algebraic knots: the links of singularity for normal complex surfaces with curves inside them. 

My work on knot lattice homology has also lead me to be interested in Floer homotopy, which attempts to model algebraic invariants such as Heegaard Floer and knot Floer as the singular homology of some spectra in an attempt to glean new invariants and obstrctions from the theories. Since Heegaard Floer and knot Floer come with the action of some extra variables, we then have a choice on how we are going to model that extra data. In the case of lattice homotopy and knot lattice homotopy this is as a filtered space, but other attempts such as that for grid homology and monopole homology use other techniques such as more generic diagrams or equivariant homology. 

I have also done work in contact topology, particularly in the study of Legendrian knots. 

Teaching:

• Fall 2024, 1 section of Math 211 (Calc 1 at IU) Instructor

• Spring 2024, 1 section of Math 311 (Calc 3 at IU), Instructor 

• Fall 2023, 2 sections of Math 211 (Calc 1 at IU), instructor 

• Fall 2022, 2 sections of Math 211 (Calc 1 at IU), Instructor

• Fall 2021, MATH 122L (Calc 2 at Duke), Instructor for course including lecturing. 

• Spring 2021, MATH 112L (Calc 2), Ran discussion section as Instructor

• Fall 2020, MATH 111L (Calc 1), Ran discussion section as Instructor

• Spring 2020, MATH 202D (Combined Linear Algebra and Multivariable Calc for Econ), Ran discussion section as TA

• Fall 2019, Grader for Smooth Manifolds and Intro to Proofs

• Fall 2018, MATH 202D (Combined Linear Algebra and Multivariable Calc for Econ), Ran two discussion sections as TA

Was secretary for the Duke AMS chapter and pervious student event coordinator for the Duke AWM chapter and.

Graduates Achieving Inclusion Now (GAIN) is a conference designed to empower both faculty and graduate students to converse about issues of discrimination and systemic inequity. We aim to equip faculty with strategies to improve their departments in a way that is positive and constructive for all members of the graduate mathematics community. Here is a link to the GAIN website. 

Anti-Racism Work at Duke

Here is a petition to the Duke Math Department on taking anti-racist action (Duke Math Anti-Racism Petition).  As of yet there has been no formal response, though correspondence says one is being made. There is also a letter to President Price written by the Duke Graduate Student Union (DGSU Racial Justice Demands) detailing how Duke as a whole can take meaningful anti-racist action. The letter include links to a number of different efforts in smaller departments and schools on campus.