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<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">UNIVERSITY OF CHICAGO</span></i><o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">COMPUTER SCIENCE DEPARTMENT</span></i><o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-size:12.0pt;font-family:Helvetica;color:#8B0102">PRESENTS</span></i><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;font-family:Helvetica">Huy Tuan Pham</span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:Helvetica">Stanford University</span></b><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;color:black">Tuesday, </span>
</b><b><span style="font-size:11.0pt">November 8<span style="color:black">, 2022 at 3:30pm</span></span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;color:black;background:yellow">Kent Chemical Laboratory, Room 107</span></b><o:p></o:p></p>
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<p style="margin:0in"><b><i><span style="font-size:12.0pt">Title:</span></i></b><span style="font-size:12.0pt">
<span style="color:black">Talagrand’s selector process conjecture and suprema of positive empirical processes</span></span><span style="font-size:10.0pt;font-family:"Helvetica Neue";color:black"> </span><o:p></o:p></p>
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<p style="margin:0in"><b><i><span style="font-size:12.0pt">Abstract:</span></i></b><b><span style="font-size:12.0pt">
</span></b><span style="font-size:12.0pt"> <span style="color:black">Understanding suprema of stochastic processes is an important subject in probability theory with many applications. While much is known in the case of Gaussian processes thanks to Talagrand’s
celebrated majorizing measure theorem, moving beyond the Gaussian case is a much more challenging quest. In this talk, I will discuss recent joint work with Jinyoung Park that resolves a conjecture of Talagrand on extreme events of suprema of certain stochastic
processes driven by sparse Bernoulli random variables (known as selector processes), and a question of Talagrand on general positive empirical processes. Combining with the recent resolution of the (generalized) Bernoulli conjecture, this gives the first steps
towards the last missing piece in the study of suprema of general empirical processes. </span></span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">The proof of Talagrand’s conjecture is combinatorial and easily leads to the proof of the Kahn-Kalai conjecture, an important question in probabilistic combinatorics and random graph theory</span><span style="font-family:"Helvetica Neue";color:black">. </span><o:p></o:p></p>
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<p><b><i><span style="font-size:12.0pt">Bio:</span></i></b><span style="font-size:12.0pt">
<span style="color:black;background:white">I am a Fourth year PhD student in the<span class="apple-converted-space"> </span></span>Department of Mathematics<span class="apple-converted-space"><span style="color:black;background:white"> </span></span><span style="color:black;background:white">at
Stanford University. I am very fortunate to be advised by Professor<span class="apple-converted-space"> </span></span>Jacob Fox<span style="color:black;background:white">. I previously obtained my BS in Mathematics and MS in Statistics with Honors and Distinction
from Stanford University, and a Master of Advanced Study in Mathematics with Distinction from the University of Cambridge. I am currently supported by a<span class="apple-converted-space"> </span></span>Two Sigma Fellowship<span style="color:black;background:white">.</span></span><o:p></o:p></p>
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<p style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;font-family:Helvetica;color:black">Host:<span class="apple-converted-space"> Alexander Razborov</span></span></b><br>
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