About me
During the spring and summer of 2024 I will be at the Ludwig Maximilian University of Munich as a Humboldt Research Fellow.
I am an associate professor of mathematics at Virginia Commonwealth University. My research interests lie primarily in the calculus of variations, partial differential equations and geometric measure theory, with a focus on problems arising from materials science, biology and physics.
I obtained my PhD from Indiana University under the supervision of Peter Sternberg. Before joining VCU, I was a Fields-Ontario postdoctoral fellow at the Fields Institute and at McMaster University working with Stan Alama and Lia Bronsard. Prior to that, I spent two years at McGill University working with Rustum Choksi and Gantumur Tsogtgerel.
My research is supported by funds from Alexander von Humboldt Foundation, National Science Foundation and Simons Foundation.
Publications
Journal Articles
A. Burchard, D. Carazzato, I. Topaloglu
Maximizers of nonlocal interactions of Wasserstein type
submitted [pdf][arXiv]
D. Carazzato, A. Pratelli, I. Topaloglu
On the existence of minimizing sets for a weakly-repulsive non-local energy
submitted [pdf][arXiv]
M. Bonacini, R. Cristoferi, I. Topaloglu
Stability of the ball for attractive-repulsive energies
SIAM J. Math. Anal. 56, 588-615 (2024) [pdf][arXiv][doi]
M. Schwitzerlett, H. R. Ogrosky, I. Topaloglu
A long-wave model for film flow inside a tube with slip
J. Fluid Mech. 974, A22 (2023) [pdf][doi]
M. Novack, I. Topaloglu, R. Venkatraman
Least Wasserstein distance between disjoint shapes with perimeter regularization
J. Funct. Anal. 284, 109732 (2023) [pdf][arXiv][doi]
R. Choksi, R. Neumayer, I. Topaloglu
Anisotropic liquid drop models
Adv. Calc. Var. 15, 109-131 (2022) [pdf][arXiv][doi]
M. Bonacini, R. Cristoferi, I. Topaloglu
Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals
J. Geom. Anal. 32, 48 (2022) [pdf][arXiv][doi]
O. Misiats, O. Stanzhytskyi, I. Topaloglu
On global existence and blowup of solutions of stochastic Keller-Segel type equation
Nonlinear Differ. Equ. Appl. 29, 3 (2022) [pdf][arXiv][doi]
M. Bonacini, R. Cristoferi, I. Topaloglu
Minimality of polytopes in a nonlocal anisotropic isoperimetric problem
Nonlinear Anal. 205, 112223 (2021) [pdf][arXiv][doi]
S. Alama, L. Bronsard, I. Topaloglu, A. Zuniga
A nonlocal isoperimetric problem with density perimeter
Calc. Var. PDEs 60, 1 (2021) [pdf][arXiv][doi]
O. Misiats, I. Topaloglu
On minimizers of an anisotropic liquid drop model
ESAIM: COCV 27, S20 (2021) [pdf][arXiv][doi]
O. Misiats, I. Topaloglu, D. Vasiliu
Singular perturbation of an elastic energy with a singular weight
Physica D 406, 132422 (2020) [pdf]arXiv][doi]
K. Craig, I. Topaloglu
Aggregation-diffusion to constrained interaction: Minimizers & gradient flows in the slow diffusion limit
Ann. Inst. Henri Poincare (C) Anal. Non Lineaire 37, 239-279 (2020) [pdf][arXiv][doi]
S. Alama, L. Bronsard, R. Choksi, I. Topaloglu
Droplet phase in a nonlocal isoperimetric problem under confinement
Comm. Pure Appl. Anal. 19, 175-202 (2020) [pdf][arXiv][doi]
S. Alama, L. Bronsard, R. Choksi, I. Topaloglu
Droplet breakup in the liquid drop model with background potential
Commun. Contemp. Math. 21, 1850022 (2019) [pdf][arXiv][doi]
R. C. Fetecau, M. Kovacic, I. Topaloglu
Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion
Discrete Contin. Dyn. Syst. Ser. B 24, 1815-1842 (2019) [pdf][arXiv][doi]
A. Burchard, R. Choksi, I. Topaloglu
Nonlocal shape optimization via interactions of attractive and repulsive potentials
Indiana Univ. Math. J. 67, 375-395 (2018) [pdf][arXiv][doi]
S. Alama, L. Bronsard, R. Choksi, I. Topaloglu
Ground-states for the liquid drop and TFDW models with long-range attraction
J. Math. Phys. 58, 103503 (2017) [pdf][arXiv][doi]
S. Alama, L. Bronsard, I. Topaloglu
Sharp interface limit of an energy modelling nanoparticle-polymer blends
Interfaces Free Bound. 18, 263-290 (2016) [pdf][arXiv][doi]
K. Craig, I. Topaloglu
Convergence of regularized nonlocal interaction energies
SIAM J. Math. Anal. 48, 34-60 (2016) [pdf][arXiv][doi]
R. Simione, D. Slepcev, I. Topaloglu
Existence of ground states of nonlocal-interaction energies
J. Stat. Phys. 159, 972-986 (2015) [pdf][arXiv][doi]
R. Choksi, R. C. Fetecau, I. Topaloglu
On minimizers of interaction functionals with competing attractive and repulsive potentials
Ann. Inst. Henri Poincare (C) Anal. Non Lineaire 32, 1283-1305 (2015) [pdf][doi]
R. Choksi, I. Topaloglu, G. Tsogtgerel
Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere
ESAIM: COCV 21, 247-270 (2015) [pdf][arXiv][doi]
I. Topaloglu
On a nonlocal isoperimetric problem on the two-sphere
Comm. Pure Appl. Anal. 12, 597-620 (2013) [pdf][doi]
P. Sternberg, I. Topaloglu
On the global minimizers of a nonlocal isoperimetric problem in two dimensions
Interfaces Free Bound. 13, 155-169 (2011) [pdf][doi]
A. Eden, I. Topaloglu
Standing waves for a generalized Davey-Stewartson system: Revisited
Appl. Math. Lett. 21, 342-347 (2008) [pdf][doi]
Review Articles and Reports
I. Topaloglu
Nonlocal variational problems on polygons
Oberwolfach Rep. 19, 2171-2174 (2022) [pdf][doi]
R. Choksi, C. B. Muratov, I. Topaloglu
An old problem resurfaces nonlocally: Gamow's liquid drops inspire today's research and applications
Notices Amer. Math. Soc. 64, 1275-1283 (2017) [pdf][doi]
Teaching
I regularly teach courses in calculus, multivariable calculus, advanced calculus, probability theory, ordinary differential equations, partial differential equations, real analysis, and measure theory.