Tianyi Zheng


IÕm an Assistant Professor in the Department of Mathematics at the UC San Diego. Before coming to UCSD in the Fall of 2016, I was a postdoc in the Department of Mathematics at Stanford University. I received Ph.D. in Mathematics from Cornell University in 2013.


My primary research interest is in random walks on groups. I'm also interested in harmonic functions on groups, metric embeddings, the 'spectral' approach to problems in geometric group theory, and mixing times of finite Markov chains that are linked to some infinite groups.



Email: tzheng2 AT math.ucsd.edu

Office: 6202 Applied Physics and Mathematics, UCSD




IÕm teaching MATH180A Fall 2018.






o   Growth of periodic Grigorchuk groups,

         with Anna Erschler. Submitted, (2018), arXiv 1802.09077.




o   Isoperimetric inequalities, shape of F{\o}lner sets and groups with ShalomÕs property H_FD,

         with Anna Erschler. Submitted, (2017), arxiv 1708.04730.



o   ShalomÕs property H_FD and extensions by \mathbb{Z} of locally finite groups,

          with Jˇrˇmie Brieussel. To appear in Israel J. Math, (2017), arxiv 1706.00707.



o   Random walks among time increasing conductances: heat kernel estimates,

          with Amir Dembo and Ruojun Huang. Submitted, (2017), arxiv 1705.07534.



o   Random walks on the discrete affine group,

          with Jˇrˇmie Brieussel and Ryokichi Tanaka. Submitted, (2017), arxiv 1703.07741.


o   On groups, slow heat kernel decay yields Liouville property and sharp entropy bounds,

          with Yuval Peres. To appear in Int. Math. Res. Notices, (2016) arXiv 1609.05174.


o   Infinitely supported Liouville measures of Schreier graphs,

          with Kate Juschenko. To appear in Group Geom. Dyn, (2016) arXiv 1608.03554 .


o   Speed of random walks, isoperimetry and compression of finitely generated groups,

          with Jˇrˇmie Brieussel. Submitted, (2015) arXiv 1510.08040 .


          with Laurent Saloff-Coste. To appear in Revista Matematica Iberoamericana (2015)  arXiv 1510.08830 .


           with Laurent Saloff-Coste. Ann. Probab. 44 (2016), no.6 arXiv 1501.05929 .


         with Laurent Saloff-Coste. Mathematics Zeitschrift, 279(3-4), 811-848. pdf .


          with Laurent Saloff-Coste Groups, Geom. Dyn, 9 (2015), no. 4 arXiv 1211.3003 .


           with Laurent Saloff-Coste Proceedings of the Conference "Talking across Fields",

           Annales de la Facult.e des Sciences de Toulouse. arXiv 1507.03551 .


            with Laurent Saloff-Coste. Electronic Journal of Probability, Vol.18, no.93.


            with Laurent Saloff-Coste. "Groups, graphs and random walks" 444Š474, 

                     London Math. Soc. Lecture Note Ser., 436, Cambridge Univ. Press, Cambridge, 2017.



 Past teaching at UCSD


MATH180A Winter 2017

MATH180C Spring 2017

MATH289A Spring 2017

MATH280A Fall 2017

MATH280B Winter 2018

MATH280C Spring 2018