## About me

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.

## Publications

**Journal Articles**

M. Bonacini, R. Cristoferi, I. Topaloglu

**Stability of the ball for attractive-repulsive energies**

submitted [pdf][arXiv]

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**

to appear in Oberwolfach Rep.[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.