Ihsan Topaloglu




Ihsan Topaloglu

Virginia Commonwealth University
Department of Mathematics
and Applied Mathematics
e-mail: iatopaloglu [chiocciola] vcu.edu

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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



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
submitted [pdf][arXiv]


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]

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]

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]



Teaching


I regularly teach courses in calculus, multivariable calculus, advanced calculus, probability theory, ordinary differential equations, partial differential equations, real analysis, and measure theory.