Summary of Research Interests
Today I predominantly work in the theory and numerics of optimal control/design for nonlocal problems, specifically in the analysis of vector-valued models arising in peridynamics, and in problems where a Lavrentiev Gap is present. However, this is quite a drastic shift from my initial research interests as an undergraduate, which were number theory and combinatorics. I expect, as a result, most of my future papers to be in numerical analysis and PDE, though I will keep researching, writing, and mentoring undergraduates in other sub-disciplines as well.
Below, the papers and talks are color coded by subject area.
Red: PDEs/numerical analysis
Purple: Combinatorics
Pink: Number theory
Green: Analysis
Black: miscellaneous
Below, the papers and talks are color coded by subject area.
Red: PDEs/numerical analysis
Purple: Combinatorics
Pink: Number theory
Green: Analysis
Black: miscellaneous
Papers
Submitted/in preparation
On Convergence of Solutions for Non-local Optimal Control Problems with Varying Fractional Parameter, in preparation.
Analysis and Finite Elements of Optimal Design in Peridynamics, in preparation.
Gamma Convergence with Discontinuous Ritz Methods for the Manià’s Problem of Lavrentiev Gap Phenomenon, in preparation.
Walking to infinity along some number theory sequences, submitted.
Accepted/in press
On the Optimal Control of a Linear Peridynamics Model. Applied Mathematics and Optimization, Volume 88 (Preprint)
Zeckendorf's theorem using indices in an arithmetic progression. Fibonacci Quarterly, Volume 59, No. 4. (PDF)
On the combinatorics of placing balls into ordered bins. INTEGERS, Volume 21. (PDF)
Central limit theorems for compound paths on the 2-dimensional lattice. Fibonacci Quarterly, Volume 58, No. 3. (PDF)
Gaussian behavior in Zeckendorf decompositions from Lattices. Fibonacci Quarterly, Volume 57, No. 3. (PDF)
Recasting the proof of Parseval's Identity: Turkish Journal of Inequalities, Issue 3 Volume 1 (July 2019) (PDF)
On Convergence of Solutions for Non-local Optimal Control Problems with Varying Fractional Parameter, in preparation.
Analysis and Finite Elements of Optimal Design in Peridynamics, in preparation.
Gamma Convergence with Discontinuous Ritz Methods for the Manià’s Problem of Lavrentiev Gap Phenomenon, in preparation.
Walking to infinity along some number theory sequences, submitted.
Accepted/in press
On the Optimal Control of a Linear Peridynamics Model. Applied Mathematics and Optimization, Volume 88 (Preprint)
Zeckendorf's theorem using indices in an arithmetic progression. Fibonacci Quarterly, Volume 59, No. 4. (PDF)
On the combinatorics of placing balls into ordered bins. INTEGERS, Volume 21. (PDF)
Central limit theorems for compound paths on the 2-dimensional lattice. Fibonacci Quarterly, Volume 58, No. 3. (PDF)
Gaussian behavior in Zeckendorf decompositions from Lattices. Fibonacci Quarterly, Volume 57, No. 3. (PDF)
Recasting the proof of Parseval's Identity: Turkish Journal of Inequalities, Issue 3 Volume 1 (July 2019) (PDF)
Presentations
An Optimal Control Problem in Peridynamics: Analysis and Discretization (Slides: jsiktar_tamu_controlv1.pdf)
Nonlocal Optimal Control Problems with Quasiconvex Energy Densities in Varying Fractional Parameter (Slides: jsiktarfraccontrolv1.pdf)
Asymptotic Compatibility of Parameterized Optimal Design Problems. Spring 2024 Finite Element Circus, Brown University, Providence, RI, April 2024. (Slides: jsiktar_brownfecircus_slidesv3.pdf)
Optimal Design of Nonlocal Problems and Asymptotic Compatibility. ICERM Workshop, Nonlocality: Challenges in Modeling and Simulation, Providence, RI, April 2024 (poster presentation) (poster.pdf)
103rd Annual MAA Southeastern Sectional Meeting: Walking to Infinity Along Some Number Theory Sequences (March 2024) (Slides: jsiktarprimewalksmaav1.pdf)
Wayne State University Applied Math Seminar (February 2024) (Slides: jsiktarwaynestates2024v1.pdf)
JMM 2024: Analysis and Discretization of Optimal Control Problems in Peridynamics (January 2024) (Slides: jsiktarjmm2024v1.pdf)
Fall 2023 Finite Element Circus (October 2023) (Slides: jsiktarnotredamev3.pdf)
SIAM Central States Meeting 2023: Analysis and Discretization of Optimal Control Problems in Peridynamics (October 2023) (Slides: jsiktarnebraska2023v1.pdf)
Carnegie Mellon University Undergraduate Math Club: Grad School Journeys: Nonlocal Edition (October 2023) (Slides)University of Pittsburgh Analysis and PDE Seminar: An Optimal Control Problem in Peridynamics: Analysis and Discretization (October 2023) (Slides)
Analytical Modeling of Piezoelectric Stack Actuators for Vibrafuge Applications (August 2023) Slides
AMS Sectional Meeting Central States: Analysis and Discretization of Optimal Control Problems in Peridynamics (April 2023) (Slides)
UTK CAM Seminar: An Optimal Control Problem in Peridynamics: Analysis and Discretization (November 2022) (Slides)
UTK Presentations Seminar: Calculus of Variations: Theory and Applications to Solid Mechanics (April 2022) (Slides)
UTK SIAM Research Showcase Competition: A Tale of Two Uniqueness Problems: Optimal Control in Solid Mechanics (March 2022) (Slides) [won 2nd place!]
UTK Presentations Seminar: An Optimal Control Problem in Peridynamics (February 2022) (Slides)
Oral Speciality Examination: An Optimization Problem in Peridynamics (November 2021) (Slides)
On the combinatorics of placing balls into ordered bins: SIAM-DM 2021 Annual Meeting (July 2021) (Slides)
UTK CAM Seminar: Asymptotically compatible schemes for discretization of nonlocal problems (April 2021) (Slides) [Review Talk]
On the combinatorics of placing balls into ordered bins: 46th Annual New York State Regional Graduate Mathematics Conference (April 2021) (Slides)
2021 Graduate Student Combinatorics Conference (April 2021) (Slides) [delivered by Vedant Bonde]
Asymptotic analysis for lattice walks derived from Zeckendorf decompositions: 2020 19th International Fibonacci Conference (July 2020) (Slides)
Integral Cauchy-Schwarz and Parseval's Identity: 2019 SIAM SEAS Regional Conference (September 2019) (Slides)
2019 Combinatorial and Additive Number Theory Conference (May 2019) (Slides) [delivered by Steven J. Miller]
2019 Joint Mathematics Meetings (January 2019) (Slides)
Gaussian behavior in Zeckendorf decompositions arising from lattices (August 2018) (Slides)
Generalizations of Zeckendorf's Theorem to Two-Dimensional Sequences (January 2018) (Slides) [also includes a Beamer template]
Nonlocal Optimal Control Problems with Quasiconvex Energy Densities in Varying Fractional Parameter (Slides: jsiktarfraccontrolv1.pdf)
Asymptotic Compatibility of Parameterized Optimal Design Problems. Spring 2024 Finite Element Circus, Brown University, Providence, RI, April 2024. (Slides: jsiktar_brownfecircus_slidesv3.pdf)
Optimal Design of Nonlocal Problems and Asymptotic Compatibility. ICERM Workshop, Nonlocality: Challenges in Modeling and Simulation, Providence, RI, April 2024 (poster presentation) (poster.pdf)
103rd Annual MAA Southeastern Sectional Meeting: Walking to Infinity Along Some Number Theory Sequences (March 2024) (Slides: jsiktarprimewalksmaav1.pdf)
Wayne State University Applied Math Seminar (February 2024) (Slides: jsiktarwaynestates2024v1.pdf)
JMM 2024: Analysis and Discretization of Optimal Control Problems in Peridynamics (January 2024) (Slides: jsiktarjmm2024v1.pdf)
Fall 2023 Finite Element Circus (October 2023) (Slides: jsiktarnotredamev3.pdf)
SIAM Central States Meeting 2023: Analysis and Discretization of Optimal Control Problems in Peridynamics (October 2023) (Slides: jsiktarnebraska2023v1.pdf)
Carnegie Mellon University Undergraduate Math Club: Grad School Journeys: Nonlocal Edition (October 2023) (Slides)University of Pittsburgh Analysis and PDE Seminar: An Optimal Control Problem in Peridynamics: Analysis and Discretization (October 2023) (Slides)
Analytical Modeling of Piezoelectric Stack Actuators for Vibrafuge Applications (August 2023) Slides
AMS Sectional Meeting Central States: Analysis and Discretization of Optimal Control Problems in Peridynamics (April 2023) (Slides)
UTK CAM Seminar: An Optimal Control Problem in Peridynamics: Analysis and Discretization (November 2022) (Slides)
UTK Presentations Seminar: Calculus of Variations: Theory and Applications to Solid Mechanics (April 2022) (Slides)
UTK SIAM Research Showcase Competition: A Tale of Two Uniqueness Problems: Optimal Control in Solid Mechanics (March 2022) (Slides) [won 2nd place!]
UTK Presentations Seminar: An Optimal Control Problem in Peridynamics (February 2022) (Slides)
Oral Speciality Examination: An Optimization Problem in Peridynamics (November 2021) (Slides)
On the combinatorics of placing balls into ordered bins: SIAM-DM 2021 Annual Meeting (July 2021) (Slides)
UTK CAM Seminar: Asymptotically compatible schemes for discretization of nonlocal problems (April 2021) (Slides) [Review Talk]
On the combinatorics of placing balls into ordered bins: 46th Annual New York State Regional Graduate Mathematics Conference (April 2021) (Slides)
2021 Graduate Student Combinatorics Conference (April 2021) (Slides) [delivered by Vedant Bonde]
Asymptotic analysis for lattice walks derived from Zeckendorf decompositions: 2020 19th International Fibonacci Conference (July 2020) (Slides)
Integral Cauchy-Schwarz and Parseval's Identity: 2019 SIAM SEAS Regional Conference (September 2019) (Slides)
2019 Combinatorial and Additive Number Theory Conference (May 2019) (Slides) [delivered by Steven J. Miller]
2019 Joint Mathematics Meetings (January 2019) (Slides)
Gaussian behavior in Zeckendorf decompositions arising from lattices (August 2018) (Slides)
Generalizations of Zeckendorf's Theorem to Two-Dimensional Sequences (January 2018) (Slides) [also includes a Beamer template]