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lang=en-us link=blue vlink="#954f72" style='tab-interval: .5in;word-wrap:break-word'> <div class=wordsection1> <p class=msonormal><span class=spelle><b style='mso-bidi-font-weight:normal'><span style='font-size:22.0pt;font-family:times'>tianyi</span></b></span><b style='mso-bidi-font-weight:normal'><span style='font-size:22.0pt;font-family: times'> zheng<o:p></o:p></span></b></p> <p class=msonormal><span style='font-size:22.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'>i am an associate 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.<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family: "times new roman";mso-bidi-font-family:arial;color:#444444;background:white'>my primary research interest is in random walks on groups. i'm also interested in harmonic functions on groups, groups of intermediate volume growth and subgroup dynamics in the <span class=spelle>chabauty</span> spaces. <o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family: "times new roman";mso-bidi-font-family:arial;color:#444444;background:white'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family: "times new roman";mso-bidi-font-family:arial;color:#444444;background:white'>here is my </span><span style='font-size:14.0pt;font-family:times'><a href="http://www.math.ucsd.edu/~tiz161/cvzheng2021.pdf">cv</a></span><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:#444444;background:white'>.</span><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:"times new roman"'><o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'>email: tzheng2 at math.ucsd.edu<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'>office: 6202 applied physics and mathematics, ucsd<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:18.0pt;font-family:times'>teaching<o:p></o:p></span></b></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'>i am teaching math 180b in winter 2022.<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:18.0pt;font-family:times'><o:p>&nbsp;</o:p></span></b></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:18.0pt;font-family:times'>articles<o:p></o:p></span></b></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:18.0pt;font-family:times'><o:p>&nbsp;</o:p></span></b></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></b></p> <p class=enumerateitem style='margin-left:.5in;text-indent:-.25in;mso-list: l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family: "courier new";mso-fareast-font-family:"courier new"'><span style='mso-list: ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i><span style='font-size:14.0pt'>asymptotic behaviors of random walks on countable groups</span></i><span style='font-size:14.0pt'>. survey article submitted to the proceedings of icm 2022. </span><span style='font-size:14.0pt;font-family: times'><a href="http://www.math.ucsd.edu/~tiz161/zheng_rwsurvey.pdf">pdf</a></span><span style='font-size:14.0pt;font-family:times;mso-bidi-font-family:arial; color:#444444;background:white'>.</span><span style='font-size:14.0pt'><o:p></o:p></span></p> <p class=enumerateitem style='margin-left:.5in'><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p> <p class=enumerateitem style='margin-left:.5in;text-indent:-.25in;mso-list: l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family: "courier new";mso-fareast-font-family:"courier new"'><span style='mso-list: ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><em><span style='font-size:14.0pt'>law of large numbers for the drift of two-dimensional wreath product</span></em><span style='font-size:14.0pt'>. with anna <span class=spelle>erschler</span>, accepted for publication in <span class=spelle><em>probab</em></span><em>. theory related fields</em>, <span class=spelle>arxiv</span>: 2011.07628 (2020).<o:p></o:p></span></p> <p class=enumerateitem style='margin-left:.5in'><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p> <p class=enumerateitem style='margin-left:.5in;text-indent:-.25in;mso-list: l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family: "courier new";mso-fareast-font-family:"courier new"'><span style='mso-list: ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><em><span style='font-size:14.0pt'>isoperimetric profiles and random walks on some groups defined by piecewise actions</span></em><span style='font-size:14.0pt'>. <span style='mso-spacerun:yes'> </span>with l. <span class=spelle>saloff-coste</span>,<em> </em>accepted for publication in <span class=spelle><em>probab</em></span><em>. theory related fields.</em> (2021).<o:p></o:p></span></p> <p class=enumerateitem><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p> <p class=enumerateitem style='margin-left:.5in;text-indent:-.25in;mso-list: l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family: "courier new";mso-fareast-font-family:"courier new"'><span style='mso-list: ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><em><span style='font-size:14.0pt'>speed of random walks, isoperimetry and compression of finitely generated groups</span></em><span style='font-size:14.0pt'>. with j. <span class=spelle>brieussel</span>, <em>ann. of math.</em> (2) 193 (2021), no. 1, 1 105.<o:p></o:p></span></p> <p class=enumerateitem><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p> <p class=enumerateitem style='margin-left:.5in;text-indent:-.25in;mso-list: l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family: "courier new";mso-fareast-font-family:"courier new"'><span style='mso-list: ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><em><span style='font-size:14.0pt'>random walks on discrete affine groups</span></em><span style='font-size:14.0pt'>. with j. <span class=spelle>brieussel</span> and r. tanaka,<em> </em>accepted for publication in <em>groups geom. <span class=spelle>dyn</span>.</em> (2021).<o:p></o:p></span></p> <p class=enumerateitem style='margin-left:.5in'><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p> <p class=msolistparagraphcxspfirst style='text-indent:-.25in;mso-list:l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'>on fc-central extensions of groups of intermediate growth, <o:p></o:p></span></i></p> <p class=msolistparagraphcxspmiddle><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'>submitted (2020), <a href="https://arxiv.org/abs/2001.07814"><span class=spelle>arxiv</span> 2001.07814</a><o:p></o:p></span></p> <p class=msolistparagraphcxspmiddle><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'><o:p>&nbsp;</o:p></span></p> <p class=msolistparagraphcxspmiddle><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'><o:p>&nbsp;</o:p></span></p> <p class=msolistparagraphcxspmiddle style='text-indent:-.25in;mso-list:l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><span class=spelle><i style='mso-bidi-font-style: normal'><span style='font-size:14.0pt;font-family:"times new roman",serif; mso-fareast-font-family:"times new roman"'>neretin</span></i></span><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'> groups admit no non-trivial invariant random subgroups,</span></i><span style='font-size:14.0pt;font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'> <i style='mso-bidi-font-style:normal'><o:p></o:p></i></span></p> <p class=msolistparagraphcxspmiddle><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'>submitted (2019), <a href="https://arxiv.org/abs/1905.07605"><span class=spelle>arxiv</span> 1905.07605</a>.<o:p></o:p></span></p> <p class=msolistparagraphcxsplast><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'><o:p>&nbsp;</o:p></span></i></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></b></p> <p class=msolistparagraphcxspfirst style='text-indent:-.25in;mso-list:l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'>on rigid stabilizers and invariant random subgroups of groups of homeomorphisms,</span></i><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'> <i style='mso-bidi-font-style:normal'><o:p></o:p></i></span></p> <p class=msolistparagraphcxspmiddle><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'>submitted (2019), <a href="https://arxiv.org/abs/1901.04428"><span class=spelle>arxiv</span> 1901.04428</a>.<o:p></o:p></span></p> <p class=msolistparagraphcxspmiddle><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'><o:p>&nbsp;</o:p></span></i></p> <p class=msolistparagraphcxspmiddle><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'><o:p>&nbsp;</o:p></span></i></p> <p class=msolistparagraphcxsplast style='text-indent:-.25in;mso-list:l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'>growth of periodic <span class=spelle>grigorchuk</span> groups,<o:p></o:p></span></i></p> <p class=msonormal><span style='font-size:14.0pt;font-family:"times new roman",serif; mso-fareast-font-family:"times new roman"'><span style='mso-spacerun:yes'>         </span>with anna <span class=spelle>erschler</span>. invent. math. 219 (2020), no.3, 1069-1155.</span><span style='font-family:"verdana",sans-serif; mso-fareast-font-family:"times new roman";mso-bidi-font-family:"times new roman"; color:black'>&nbsp;</span><span style='font-family:"times new roman",serif; mso-fareast-font-family:"times new roman"'> </span><span style='font-size:14.0pt; font-family:"times new roman",serif;mso-fareast-font-family:"times new roman"'><a href="https://arxiv.org/abs/1802.09077"><span class=spelle>arxiv</span> 1802.09077</a>.</span><span style='font-family:"times new roman",serif; mso-fareast-font-family:"times new roman"'><o:p></o:p></span></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></b></p> <p class=msolistparagraph style='text-indent:-.25in;mso-list:l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'>isoperimetric inequalities, shape of f{\<span class=grame>o}<span class=spelle>lner</span></span> sets and groups with <span class=spelle>shaloms</span> property h_fd,<o:p></o:p></span></i></p> <p class=msonormal><span style='font-size:14.0pt;font-family:"times new roman",serif; mso-fareast-font-family:"times new roman"'><span style='mso-spacerun:yes'>         </span>with anna <span class=spelle>erschler</span>. to appear in ann. inst. fourier (grenoble) (2017), <a href="https://arxiv.org/abs/1708.04730"><span class=spelle>arxiv</span> 1708.04730</a>.<o:p></o:p></span></p> <p class=msolistparagraph><span style='font-size:14.0pt;font-family:"times new roman",serif; mso-fareast-font-family:"times new roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:"times new roman",serif; mso-fareast-font-family:"times new roman"'><o:p>&nbsp;</o:p></span></p> <p class=msolistparagraph style='text-indent:-.25in;mso-list:l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><span class=spelle><span class=grame><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'>shalom s</span></i></span></span><span class=grame><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt; font-family:"times new roman",serif;mso-fareast-font-family:"times new roman"'> <span style='mso-spacerun:yes'> </span>property</span></i></span><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: "times new roman",serif;mso-fareast-font-family:"times new roman"'> h_fd and extensions by \<span class=spelle>mathbb</span>{z} of locally finite groups,<o:p></o:p></span></i></p> <p class=msonormal><span style='font-size:14.0pt;font-family:"times new roman",serif'><span style='mso-spacerun:yes'>          </span><span style='color:black;mso-color-alt: windowtext;background:white'>with <span class=spelle>jrmie</span>&nbsp;<span class=spelle>brieussel</span>. israel j. math, (2018), <a href="https://arxiv.org/abs/1706.00707"><span class=spelle><span style='mso-fareast-font-family:"times new roman"'>arxiv</span></span><span style='mso-fareast-font-family:"times new roman"'> 1706.00707</span></a>.</span><span style='background:white'><o:p></o:p></span></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:"times new roman",serif; background:white'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:"times new roman",serif; color:black;mso-color-alt:windowtext;background:white'><span style='mso-spacerun:yes'>     </span></span><span style='font-size:14.0pt; font-family:"times new roman",serif;background:white'><o:p></o:p></span></p> <p class=msolistparagraph style='text-indent:-.25in;mso-list:l6 level1 lfo1'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:"times new roman",serif;color:black; mso-color-alt:windowtext;background:white'>random walks among time increasing <span class=spelle>conductances</span>: heat kernel estimates,</span></i><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: "times new roman",serif;background:white'><o:p></o:p></span></i></p> <p class=msonormal><span style='font-size:14.0pt;font-family:"times new roman",serif; color:black;mso-color-alt:windowtext;background:white'><span style='mso-spacerun:yes'>          </span>with amir dembo and <span class=spelle>ruojun</span> huang. <span class=spelle>probab</span>. theory <span class=spelle>relat</span>. fields, (2018), <a href="https://arxiv.org/abs/1705.07534"><span class=spelle>arxiv</span> 1705.07534</a>.</span><span style='font-family:"times new roman",serif; mso-fareast-font-family:"times new roman"'><o:p></o:p></span></p> <p class=msonormal style='margin-left:.25in'><span style='font-size:14.0pt; font-family:"times new roman",serif;mso-fareast-font-family:"times new roman"; color:black;background:white'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l10 level1 lfo3;background:white'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"; color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black'>on groups, slow heat kernel decay yields liouville property and sharp entropy bounds</span></i><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black'>,</span><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; with yuval peres. int. math. res. notices, rny034, (2018)&nbsp;</span><span class=spelle><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:#7f6000;mso-themecolor:accent4;mso-themeshade: 128;mso-style-textfill-fill-color:#7f6000;mso-style-textfill-fill-themecolor: accent4;mso-style-textfill-fill-alpha:100.0%;mso-style-textfill-fill-colortransforms: lumm=50000;background:white'><a href="https://arxiv.org/abs/1609.05174"><span style='color:#7f6000;mso-themecolor:accent4;mso-themeshade:128;mso-style-textfill-fill-color: #7f6000;mso-style-textfill-fill-themecolor:accent4;mso-style-textfill-fill-alpha: 100.0%;mso-style-textfill-fill-colortransforms:lumm=50000'>arxiv</span><span style='color:#7f6000;mso-themecolor:accent4;mso-themeshade:128;mso-style-textfill-fill-color: #7f6000;mso-style-textfill-fill-themecolor:accent4;mso-style-textfill-fill-alpha: 100.0%;mso-style-textfill-fill-colortransforms:lumm=50000'> 1609.0</span><span style='color:#7f6000;mso-themecolor:accent4;mso-themeshade:128;mso-style-textfill-fill-color: #7f6000;mso-style-textfill-fill-themecolor:accent4;mso-style-textfill-fill-alpha: 100.0%;mso-style-textfill-fill-colortransforms:lumm=50000'>5174</span></a></span></span><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black;background:white'>.<o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l10 level1 lfo3;background:white'><![if !supportlists]><span style='font-size:14.0pt;font-family:"courier new";mso-fareast-font-family:"courier new"; color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black'>infinitely supported liouville measures of schreier graphs</span></i><span style='font-size:14.0pt;font-family:times; mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>,</span><span style='font-size:14.0pt;font-family:times; mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; with kate <span class=spelle>juschenko</span>. group geom. <span class=spelle>dyn</span>, 12, (2018), no.3 &nbsp;<span class=spelle><a href="http://arxiv.org/abs/1608.03554"><span style='color:#8a8c50'>arxiv</span><span style='color:#8a8c50'> 1608.03554</span></a></span>&nbsp;.<o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l7 level1 lfo4;tab-stops:list .5in; background:white'><![if !supportlists]><span style='font-size:10.0pt; mso-bidi-font-size:14.0pt;font-family:"courier new";mso-fareast-font-family: "courier new";color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: times;mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>isoperimetric profiles and random walks on some permutation wreath products</span></i><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family: "times new roman";mso-bidi-font-family:arial;color:black'>,&nbsp;</span><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; with laurent <span class=spelle>saloff-coste</span>. <span class=spelle>revista</span> <span class=spelle>matematica</span> <span class=spelle>iberoamericana</span>, 34 (2018), no.2 &nbsp;<span class=spelle><a href="http://arxiv.org/abs/1510.08830" target="_blank"><span style='color:#8a8c50'>arxiv</span><span style='color:#8a8c50'> 1510.08830</span></a></span>&nbsp;.<o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l1 level1 lfo5;tab-stops:list .5in; background:white'><![if !supportlists]><span style='font-size:10.0pt; mso-bidi-font-size:14.0pt;font-family:"courier new";mso-fareast-font-family: "courier new";color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: times;mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>random walks and isoperimetric profiles under moment conditions</span></i><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black'>,</span><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;with laurent <span class=spelle>saloff-coste</span>. ann. <span class=spelle>probab</span>. 44 (2016), no.6 <a href="http://arxiv.org/abs/1501.05929" target="_blank"><span class=spelle><span style='color:#8a8c50'>arxiv</span></span><span style='color:#8a8c50'> 1501.05929</span></a>&nbsp;.<o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l3 level1 lfo6;tab-stops:list .5in; background:white'><![if !supportlists]><span style='font-size:10.0pt; mso-bidi-font-size:14.0pt;font-family:"courier new";mso-fareast-font-family: "courier new";color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: times;mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>random walks on free solvable groups</span></i><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black'>,</span><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;with laurent <span class=spelle>saloff-coste</span>. <span class=spelle>mathematische</span> <span class=spelle>zeitschrift</span>, 279(3-4), 811-848.&nbsp;<a href="https://sites.google.com/site/tianyizhengmath/fsol.pdf?attredirects=0&amp;d=1" target="_blank"><span style='color:#8a8c50'>pdf</span></a>&nbsp;.<o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l2 level1 lfo7;tab-stops:list .5in; background:white'><![if !supportlists]><span style='font-size:10.0pt; mso-bidi-font-size:14.0pt;font-family:"courier new";mso-fareast-font-family: "courier new";color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: times;mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>random walks on nilpotent groups driven by measures supported on&nbsp;powers of generators</span></i><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black'>,</span><span style='font-size:14.0pt;font-family:times; mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</span><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black'>with laurent <span class=spelle>saloff-coste</span>.&nbsp;<span style='background:white'> groups, geom. <span class=spelle>dyn</span>, 9 (2015), no. 4&nbsp;<span class=spelle><a href="http://arxiv.org/abs/1211.3003" target="_blank"><span style='color:#8a8c50'>arxiv</span><span style='color: #8a8c50'> 1211.3003</span></a></span>&nbsp;.<o:p></o:p></span></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo8;tab-stops:list .5in; background:white'><![if !supportlists]><span style='font-size:10.0pt; mso-bidi-font-size:14.0pt;font-family:"courier new";mso-fareast-font-family: "courier new";color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: times;mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>random walks under slowly varying moment conditions on groups of polynomial volume growth</span></i><span style='font-size:14.0pt;font-family: times;mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>,</span><span style='font-size:14.0pt;font-family:times; mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;with laurent <span class=spelle>saloff-coste</span>.&nbsp;</span><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black'> proceedings of the conference &quot;talking across fields&quot;,</span><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</span><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:black'>annales de la <span class=spelle>faculte</span> des sciences de&nbsp;toulouse.&nbsp;<span class=spelle><a href="http://arxiv.org/abs/1507.03551" target="_blank"><span style='color:#8a8c50'>arxiv</span><span style='color:#8a8c50'> 1507.03551</span></a></span>&nbsp;.<o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l8 level1 lfo9;tab-stops:list .5in; background:white'><![if !supportlists]><span style='font-size:10.0pt; mso-bidi-font-size:14.0pt;font-family:"courier new";mso-fareast-font-family: "courier new";color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: times;mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>large deviations for stable like random walks on <span class=spelle>z^d</span>&nbsp;with applications to random walks on wreath products</span></i><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family: "times new roman";mso-bidi-font-family:arial;color:black'>,</span><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family:"times new roman"; mso-bidi-font-family:arial;color:#444444'><o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; with laurent <span class=spelle>saloff-coste</span>. electronic journal of probability, vol.</span><span style='font-size:14.0pt;font-family:times; mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>18, no.93.<o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p>&nbsp;</o:p></span></p> <p class=msonormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:.5in;text-indent:-.25in;mso-list:l9 level1 lfo10;tab-stops:list .5in; background:white'><![if !supportlists]><span style='font-size:10.0pt; mso-bidi-font-size:14.0pt;font-family:"courier new";mso-fareast-font-family: "courier new";color:#444444'><span style='mso-list:ignore'>o<span style='font:7.0pt "times new roman"'>&nbsp;&nbsp; </span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family: times;mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:black'>on some random walks driven by spread-out measures <span class=spelle>measures</span></span></i><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:black'>,</span><span style='font-size:14.0pt;font-family:times; mso-fareast-font-family:"times new roman";mso-bidi-font-family:arial; color:#444444'><o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family: "times new roman";mso-bidi-font-family:arial;color:black;background:white'>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; with laurent <span class=spelle>saloff-coste</span>. &quot;groups, graphs and random walks&quot; </span><span style='font-family: "verdana",sans-serif;mso-fareast-font-family:"times new roman";mso-bidi-font-family: "times new roman";color:black;background:white'>444474,&nbsp;</span><span style='font-family:"times new roman",serif;mso-fareast-font-family:"times new roman"'><o:p></o:p></span></p> <p class=msonormal><span style='font-family:"times new roman",serif;mso-fareast-font-family: "times new roman"'><span style='mso-spacerun:yes'>                     </span>london math. soc. lecture note ser., 436,<span style='color:black; background:white'>&nbsp;<i>cambridge univ. press, cambridge,</i>&nbsp;2017.<o:p></o:p></span></span></p> <p class=msonormal><span style='font-family:"times new roman",serif;mso-fareast-font-family: "times new roman";color:black;background:white'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-family:"times new roman",serif;mso-fareast-font-family: "times new roman";color:black;background:white'>&nbsp;</span><span style='font-family:"times new roman",serif;mso-fareast-font-family:"times new roman"'><o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times;mso-fareast-font-family: "times new roman";mso-bidi-font-family:arial;color:black'>&nbsp;</span><b style='mso-bidi-font-weight:normal'><span style='font-size:18.0pt;font-family: times'>past teaching at ucsd<o:p></o:p></span></b></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:18.0pt;font-family:times'><o:p>&nbsp;</o:p></span></b></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><a href="http://www.math.ucsd.edu/~tiz161/180aw17.html">math180a</a> winter 2017<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><a href="http://www.math.ucsd.edu/~tiz161/180cs17.html">math180c</a> spring 2017<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><a href="http://www.math.ucsd.edu/~tiz161/289a.html">math289a</a> spring 2017<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><a href="http://www.math.ucsd.edu/~tiz161/280af17.html">math280a</a> fall 2017<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><a href="http://www.math.ucsd.edu/~tiz161/280bw18.html">math280b</a> winter 2018<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><a href="http://www.math.ucsd.edu/~tiz161/280cs18.html">math280c</a> spring 2018<o:p></o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><span style='font-size:14.0pt;font-family:times'>.<o:p></o:p></span></p> <p class=msonormal style='background:white'><span style='font-size:14.0pt; font-family:times;mso-fareast-font-family:"times new roman";mso-bidi-font-family: arial;color:#444444'><o:p>&nbsp;</o:p></span></p> <p class=msonormal><b style='mso-bidi-font-weight:normal'><span style='font-size:18.0pt;font-family:times'><o:p>&nbsp;</o:p></span></b></p> </div> </body> </html>