My research is partially supported by NSF Grants DMS1411857, DMS1715418, and NSF CAREER Grant DMS1846745.
 Small scale formations in the incompressible porous media equation, with A. Kiselev, preprint.
 Remarks on stationary and uniformlyrotating vortex sheets: Rigidity results, with J. GómezSerrano, J. Park and J. Shi, preprint.
 Remarks on stationary and uniformlyrotating vortex sheets: Flexibility results, with J. GómezSerrano, J. Park and J. Shi, preprint.
 Sharp stability for the interaction energy, with X. Yan, preprint.
 Chemotaxis and reactions in biology, with A. Kiselev, F. Nazarov and L. Ryzhik, to appear in J. Eur. Math. Soc.
 Symmetry of hypersurfaces with ordered mean curvature in one direction, with Y.Y. Li and X. Yan, preprint.
 Uniqueness and nonuniqueness of steady states of aggregationdiffusion equations, with M. Delgadino and X. Yan, to appear in Comm. Pure Appl. Math.
 Symmetry in stationary and uniformlyrotating solutions of active scalar equations, with J. GómezSerrano, J. Park and J. Shi, to appear in Duke Math Journal.
 Aggregationdiffusion equations: dynamics, asymptotics, and singular limits, with J. Carrillo and K. Craig, Active Particles, Volume 2, 65108, 2019.
 Nonlinear AggregationDiffusion Equations: Radial Symmetry and Long Time Asymptotics, with J. Carrillo, S. Hittmeir and B. Volzone, Invent. Math., 218 (3), 889977.
 Congested aggregation via Newtonian interaction, with K. Craig and I. Kim, Arch. Ration. Mech. Anal., 227(1): 167, 2018.
 Finite time singularity formation for the modified SQG patch equation, with A. Kiselev, L. Ryzhik and A. Zlatoš, Ann. of Math., 184(3): 909948, 2016.
 Local regularity for the modified SQG patch equation, with A. Kiselev and A. Zlatoš, Comm. Pure Appl. Math., 70(7): 12531315, 2017.
 On the finitetime blowup of a 1D model for the 3D axisymmetric Euler equations, with K. Choi, T. Hou, A. Kiselev, G. Luo and V. Sverak, Comm. Pure Appl. Math., 70(11): 22182243, 2017.
 Mixing and unmixing by incompressible flows, with A. Zlatoš, J. Eur. Math. Soc., 19(7): 1911–1948, 2017.
 Finite time blow up for a 1D model of 2D Boussinesq system, with K. Choi and A. Kiselev, Commun. Math. Phys.,334: 16671679, 2015.
 Quasistatic evolution and congested crowd transport, with D. Alexander and I. Kim, Nonlinearity, 27: 136, 2014.
 Confinement for repulsiveattractive kernels, with D. Balagué and J. A. Carrillo, Discret. Contin. Dyn. S. Ser. B, 19: 12271248, 2014.
 Asymptotic behavior for critical PatlakKellerSegel model and an repulsiveattractive aggregation equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31(1): 81101, 2014.
 Blowup dynamics for the aggregation equation with degenerate diffusion, with A. L. Bertozzi, Physica D, special issue on Emergent behaviour in multiparticle systems with nonlocal interactions, 260: 7789, 2013.
 An aggregation equation with degenerate diffusion: qualitative property of solutions, with L. Chayes and I. Kim, SIAM J. Math. Anal, 45(5):25973049, 2013.
 The PatlakKellerSegel model and its variations: properties of solutions via maximum principle, with I. Kim, SIAM J. Math. Anal., 44(2):568602, 2012.
