{"id":208,"date":"2023-09-30T16:17:51","date_gmt":"2023-09-30T23:17:51","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/zhanhu\/?page_id=208"},"modified":"2026-11-01T11:51:55","modified_gmt":"2026-11-01T19:51:55","slug":"research","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/ivan\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p><!-- Research page body, styled from the original content and the teaching-page contents pattern. Replace the current body only; retain the site's header, page title, navigation, and footer. Before publishing, substitute the public media URLs for these three placeholders: REPLACE_WITH_CARD_SHUFFLING_SLIDES_URL REPLACE_WITH_THIRD_BRIDGE_SLIDES_URL REPLACE_WITH_THIRD_BRIDGE_NOTES_URL Use the same three appendix-free PDFs supplied previously. Existing wording, material links, course records, and CV-based talk entries are retained. Dates are the supplied October 31, 2026 snapshot; no automatic event updates are implied. Paste into a Custom HTML block; the small scoped style block handles mobile layout\/focus. --><\/p>\n<style> \/* Scoped to this page body. Site navigation, page title, and footer are untouched. *\/ #ivan-research { box-sizing: border-box; } #ivan-research *, #ivan-research *::before, #ivan-research *::after { box-sizing: border-box; } #ivan-research a { font-weight: 400; } #ivan-research #graduate-courses details a { color: #0b5f84; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px; } #ivan-research a:hover { color: #084762 !important; } #ivan-research a:focus-visible, #ivan-research [tabindex]:focus-visible { outline: 2px solid #0b5f84; outline-offset: 5px; border-radius: 2px; } #ivan-research .ir-button:hover { color: #fff !important; background: #084762 !important; } #ivan-research .ir-toc a:hover { background: #edf5f7; } #ivan-research .ir-section, #ivan-research .ir-subheading, #ivan-research #research-contents { scroll-margin-top: 110px; } #ivan-research .ir-section-header { display: flex; align-items: baseline; justify-content: space-between; gap: 16px; } #ivan-research .ir-back { flex: 0 0 auto; } #ivan-research .ir-course-table tr:last-child td { border-bottom: 0 !important; } #ivan-research .ir-meta a { font-size: inherit; } @media (max-width: 560px) { #ivan-research .ir-quote { padding: 20px !important; } #ivan-research .ir-card { padding: 22px 20px !important; } #ivan-research .ir-toc a { padding: 13px 10px !important; font-size: 14px !important; } #ivan-research .ir-toc-title { padding: 16px 18px 12px !important; } #ivan-research .ir-section { margin-top: 38px !important; } #ivan-research .ir-section-header { align-items: baseline; } #ivan-research .ir-back { font-size: 12px !important; } #ivan-research .ir-entry { padding-left: 0 !important; padding-right: 0 !important; } #ivan-research .ir-course-table, #ivan-research .ir-course-table tbody { display: block; width: 100%; } #ivan-research .ir-course-table thead { position: absolute; width: 1px; height: 1px; overflow: hidden; clip-path: inset(50%); } #ivan-research .ir-course-table tbody tr { display: block; padding: 15px 16px; border-bottom: 1px solid #e3e9eb; } #ivan-research .ir-course-table tbody tr:last-child { border-bottom: 0; } #ivan-research .ir-course-table tbody td { display: block; width: auto !important; padding: 0 !important; border: 0 !important; } #ivan-research .ir-course-table .ir-course-code { color: #0b5f84; margin-bottom: 3px; } #ivan-research .ir-course-table .ir-course-terms { margin-top: 4px; } } @media print { #ivan-research .ir-toc, #ivan-research .ir-back { display: none; } #ivan-research .ir-card, #ivan-research .ir-quote { box-shadow: none !important; } #ivan-research .ir-entry, #ivan-research .ir-section-header { break-inside: avoid; } } <\/style>\n<div id=\"ivan-research\" style=\"width: 100%; max-width: 900px; margin: 0 auto; color: #30383b; font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.75; font-weight: 400; overflow-wrap: break-word;\">\n<div class=\"ir-quote\" style=\"background-color: #c1efde; border: 2px solid #57a99a; border-radius: 10px; padding: 26px 28px; margin: 0 0 28px; font-family: 'Times New Roman', serif; box-shadow: 0 3px 10px rgba(0,0,0,.08);\">\n<p style=\"margin: 0; font-size: 18px; line-height: 1.65; color: #333333; text-indent: 20px;\">\u201cWhen we stand taller, we see farther, and a boundary that dominated the foreground can lose its importance in the larger view.\u201d<\/p>\n<p style=\"margin: 16px 0 0; font-size: 16px; line-height: 1.5; font-style: italic; color: #333333; text-align: right;\"><span style=\"color: #000000;\">\u2014 Ivan Z. Feng, <a href=\"https:\/\/imathman.medium.com\/teaching-and-research-are-the-same-thing-0f6c1dc8c1e7\" target=\"_blank\" rel=\"noopener\"><em>Teaching and Research Are the Same Thing<\/em><\/a><\/span><\/p>\n<\/div>\n<div style=\"display: flex; justify-content: center;\">\n<div style=\"max-width: 640px; border: 1px solid #e5e7eb; border-radius: 14px; padding: 16px 18px; background: #fff; box-shadow: 0 6px 18px rgba(0,0,0,.06);\" role=\"region\" aria-labelledby=\"update-title\">\n<div style=\"display: flex; align-items: center; gap: 10px; margin-bottom: 8px;\">\n      <span id=\"update-title\" style=\"display: inline-block; font: 600 12px\/1 -apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica,Arial,sans-serif; letter-spacing: .08em; text-transform: uppercase; color: #0b6ea9; background: #e0f2fe; border: 1px solid #93c5fd; border-radius: 999px; padding: 6px 10px;\">Upcoming talk<\/span>\n    <\/div>\n<p style=\"margin: 0 0 6px 0; font: 500 16px\/1.55 -apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica,Arial,sans-serif; color: #111827;\">\n      <em>Explicit Cutoff Profiles for Colored Top-m-to-Random Shuffles<\/em><br \/>\n      AMS Fall Western Sectional Meeting, Arizona State University\n    <\/p>\n<p style=\"margin: 0 0 14px 0; font: 400 13px\/1.4 -apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica,Arial,sans-serif; color: #6b7280;\">\n      Sunday, <time datetime=\"2026-11-08\">November 8, 2026<\/time>\n    <\/p>\n<p style=\"margin:0;line-height:1;\"><a href=\"#seminars-and-talks\" style=\"display: inline-block; text-decoration: none; background: #0B5F84; color: #fff; border-radius: 10px; padding: 10px 14px; font: 600 14px\/1 -apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica,Arial,sans-serif;\">Seminars and talks &rarr;<\/a><\/p>\n<\/p><\/div>\n<\/div>\n<p style=\"margin: 0 0 18px; font-size: 16px; line-height: 1.8;\">My primary research areas are probability (Markov chain theory) and algebraic combinatorics. Currently, I&#8217;m working on Burnside processes, mixing times, and card shuffling with my advisor, Prof. <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/dornsife.usc.edu\/jason-fulman\/\" target=\"_blank\" rel=\"noopener\">Jason Fulman<\/a>. I am also collaborating with <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/www.jepaguyo.com\/\" target=\"_blank\" rel=\"noopener\">J. E. Paguyo<\/a> on a twisted Bose-Einstein Markov chain and its applications to sampling Catalan structures.<\/p>\n<p style=\"margin: 0 0 18px; font-size: 16px; line-height: 1.8;\">I also like analytic number theory and algebraic geometry. In particular, I&#8217;m interested in the <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/en.wikipedia.org\/wiki\/Riemann_zeta_function\" target=\"_blank\" rel=\"noopener\">Riemann zeta function<\/a> and its related topics, which basically include contour integration and infinite products in complex analysis, L-functions and the prime number theorem in analytic number theory, the Lichtenbaum conjectures in algebraic K-theory, and the Weil conjectures in \u00e9tale cohomology.<\/p>\n<nav id=\"research-contents\" class=\"ir-toc\" style=\"margin: 30px 0 6px; border: 1px solid #d6e3e7; border-radius: 12px; overflow: hidden; background: #f6fafb;\" aria-labelledby=\"research-contents-title\">\n<h2 id=\"research-contents-title\" class=\"ir-toc-title\" style=\"margin: 0; padding: 18px 22px 14px; color: #273b44; font-size: 17px; line-height: 1.4; font-weight: 600; text-align: center;\">Table of Contents<\/h2>\n<table style=\"width: 100%; table-layout: fixed; border-collapse: collapse; border: 0; margin: 0; background: transparent;\" role=\"presentation\">\n<tbody>\n<tr>\n<td style=\"width: 50%; border: 0; border-top: 1px solid #dce8eb; padding: 0; vertical-align: middle; text-align: center;\"><a style=\"display: block; padding: 13px 16px; color: #0b5f84; font-size: 15px; line-height: 1.6; font-weight: 400; text-decoration: none;\" href=\"#selected-papers\">Selected papers<\/a><\/td>\n<td style=\"width: 50%; border: 0; border-top: 1px solid #dce8eb; border-left: 1px solid #dce8eb; padding: 0; vertical-align: middle; text-align: center;\"><a style=\"display: block; padding: 13px 16px; color: #0b5f84; font-size: 15px; line-height: 1.6; font-weight: 400; text-decoration: none;\" href=\"#seminars-and-talks\">Seminars and talks<\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; border: 0; border-top: 1px solid #dce8eb; padding: 0; vertical-align: middle; text-align: center;\"><a style=\"display: block; padding: 13px 16px; color: #0b5f84; font-size: 15px; line-height: 1.6; font-weight: 400; text-decoration: none;\" href=\"#coursework-notes\">Selected coursework notes<\/a><\/td>\n<td style=\"width: 50%; border: 0; border-top: 1px solid #dce8eb; border-left: 1px solid #dce8eb; padding: 0; vertical-align: middle; text-align: center;\"><a style=\"display: block; padding: 13px 16px; color: #0b5f84; font-size: 15px; line-height: 1.6; font-weight: 400; text-decoration: none;\" href=\"#graduate-courses\">Graduate courses<\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; border: 0; border-top: 1px solid #dce8eb; padding: 0; vertical-align: middle; text-align: center;\"><a style=\"display: block; padding: 13px 16px; color: #0b5f84; font-size: 15px; line-height: 1.6; font-weight: 400; text-decoration: none;\" href=\"#other-work\">Other fun work<\/a><\/td>\n<td style=\"width: 50%; border: 0; border-top: 1px solid #dce8eb; border-left: 1px solid #dce8eb; padding: 0; vertical-align: middle; text-align: center;\"><a style=\"display: block; padding: 13px 16px; color: #0b5f84; font-size: 15px; line-height: 1.6; font-weight: 400; text-decoration: none;\" href=\"#research-statement\">Research statement<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/nav>\n<section id=\"selected-papers\" class=\"ir-section\" style=\"margin-top: 46px;\" aria-labelledby=\"selected-papers-title\">\n<div class=\"ir-section-header\" style=\"padding-bottom: 13px; margin-bottom: 25px; border-bottom: 1px solid #ccdce2;\">\n<h2 id=\"selected-papers-title\" style=\"margin: 0; padding: 0; color: #273b44; font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; font-size: 21px; line-height: 1.4; font-weight: 600; letter-spacing: 0; text-transform: none;\">Selected papers<\/h2>\n<p><a class=\"ir-back\" style=\"color: #627880; font-size: 12px; line-height: 1.5; font-weight: 400; text-decoration: none; white-space: nowrap;\" href=\"#research-contents\" aria-label=\"Back to table of contents\">\u2191 Contents<\/a><\/p>\n<\/div>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/link.springer.com\/article\/10.1007\/s10959-026-01539-9\" target=\"_blank\" rel=\"noopener\">The Dual Burnside Process<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">[<em>Journal of Theoretical Probability<\/em> 39, article 78 (2026); published 8\/27\/2026; <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/arxiv.org\/abs\/2510.25202\" target=\"_blank\" rel=\"noopener\">arXiv<\/a>]<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/arxiv.org\/abs\/2605.16244\" target=\"_blank\" rel=\"noopener\">Analysis of a twisted Bose-Einstein Markov chain with applications to sampling Catalan structures<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">(joint work with J. E. Paguyo; 5\/15\/2026, 8\/22\/2026)<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/arxiv.org\/abs\/2604.09933\" target=\"_blank\" rel=\"noopener\">Explicit cutoff profiles for colored top-m-to-random shuffles<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">(4\/10\/2026, 5\/27\/2026; <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2026\/05\/Notes_colored_top_m_to_random_shuffles.pdf\" target=\"_blank\" rel=\"noopener\">companion notes and special examples<\/a>)<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/arxiv.org\/abs\/2606.29530\" target=\"_blank\" rel=\"noopener\">Cutoff profiles for colored top-m-to-random shuffles with growing block size<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">(6\/28\/2026)<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/scholarship.claremont.edu\/jhm\/vol16\/iss1\/23\/\" target=\"_blank\" rel=\"noopener\">The Math Teaching Atlas: Trails, Anchors, and Compass in Action<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">[Published in the <em>Journal of Humanistic Mathematics<\/em>, Volume 16, Issue 1, 344\u2013364 (January 2026); <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/arxiv.org\/abs\/2504.04313\" target=\"_blank\" rel=\"noopener\">expanded arXiv version<\/a>]<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/arxiv.org\/abs\/2502.10690\" target=\"_blank\" rel=\"noopener\">Periodicity Uncovered: A Deep Dive into Bott\u2019s Theorems in K-Theory and Fiber Bundles<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">(5\/10\/2023)<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/digitallibrary.usc.edu\/asset-management\/2A3BF1RP1MQF8\" target=\"_blank\" rel=\"noopener\">Zeta Functions: From Prime Numbers to K-Theory<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">(Master&#8217;s thesis, 5\/2022)<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1ac447Ymh0Kvk3tkxqZXH7qv9XviTQaJD\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Values of Zeta Functions at Integers<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\"><span class=\"fontstyle0\"> (1\/21\/2022)<\/span><\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/16WQQwaY6vJxKpckD0s_b_RvEPxZ_QGjr\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">A Coherent Introduction to Algebraic K-Theory<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\"><span class=\"fontstyle0\"> (11\/20\/2021)<\/span><\/span><\/p>\n<p style=\"margin: 8px 0 12px; text-align: center; font-size: 15px;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/arxiv.org\/search\/math?searchtype=author&amp;query=Feng,+I+Z\" target=\"_blank\" rel=\"noopener\">Ivan&#8217;s preprints on arXiv<\/a><\/p>\n<p style=\"margin: 0; text-align: center; color: #59656c; font-size: 15px;\">More papers coming soon&#8230; <span style=\"font-size: 1.17em;\">\ud83d\ude3a<\/span><\/p>\n<\/section>\n<section id=\"seminars-and-talks\" class=\"ir-section\" style=\"margin-top: 46px;\" aria-labelledby=\"seminars-and-talks-title\">\n<div class=\"ir-section-header\" style=\"padding-bottom: 13px; margin-bottom: 25px; border-bottom: 1px solid #ccdce2;\">\n<h2 id=\"seminars-and-talks-title\" style=\"margin: 0; padding: 0; color: #273b44; font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; font-size: 21px; line-height: 1.4; font-weight: 600; letter-spacing: 0; text-transform: none;\">Seminars and talks<\/h2>\n<p><a class=\"ir-back\" style=\"color: #627880; font-size: 12px; line-height: 1.5; font-weight: 400; text-decoration: none; white-space: nowrap;\" href=\"#research-contents\" aria-label=\"Back to table of contents\">\u2191 Contents<\/a><\/p>\n<\/div>\n<h3 id=\"upcoming-talks\" class=\"ir-subheading\" style=\"margin: 0 0 24px; color: #59656c; font-size: 16px; line-height: 1.5; font-weight: 400; text-align: center;\"><em>Upcoming<\/em><\/h3>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>Explicit Cutoff Profiles for Colored Top-m-to-Random Shuffles<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">AMS Fall Western Sectional Meeting, Arizona State University (November 8, 2026).<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>Analysis of a Twisted Bose\u2013Einstein Markov Chain with Applications to Sampling Catalan Structures<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">UC San Diego Probability Seminar (November 19, 2026).<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>Explicit Cutoff Profiles for Colored Top-m-to-Random Shuffles<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">UC Irvine Combinatorics and Probability Seminar (December 7, 2026).<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>Analysis of a Twisted Bose\u2013Einstein Markov Chain with Applications to Sampling Catalan Structures<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">Joint Mathematics Meetings, Chicago (January 14, 2027).<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>The Dual Burnside Process<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">Claremont ANTC Seminar (February 2, 2027).<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>The Math Teaching Atlas: Great Teaching Leaves Trails<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">Research Council on Mathematics Learning Annual Conference, Williamsburg, Virginia (March 11\u201313, 2027).<\/span><\/p>\n<h3 id=\"past-talks\" class=\"ir-subheading\" style=\"margin: 34px 0 24px; color: #59656c; font-size: 16px; line-height: 1.5; font-weight: 400; text-align: center;\"><em>Past talks and materials<\/em><\/h3>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>Explicit Cutoff Profiles for Colored Top-m-to-Random Shuffles<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">UC Davis Probability Seminar (October 22, 2026)<\/span><span class=\"ir-resources\" style=\"display: block; margin-top: 8px; font-size: 14px; line-height: 1.85; font-weight: 400;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1drPZGwKZygqqi5P9C9R7XCAwc3ke7MQh\/view\" target=\"_blank\" rel=\"noopener\">What the Deck Remembers: Slides<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2026\/05\/Notes_colored_top_m_to_random_shuffles.pdf\" target=\"_blank\" rel=\"noopener\">Companion Notes<\/a><\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>The Third Bridge: From Cut-and-Paste Chains to Burnside Spectra<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">USC Graduate Colloquium (October 13, 2026)<\/span><span class=\"ir-resources\" style=\"display: block; margin-top: 8px; font-size: 14px; line-height: 1.85; font-weight: 400;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/187OOF_0vmvbnmBK-T7Mxs03SDpT1FBTA\/view\" target=\"_blank\" rel=\"noopener\">Slides<\/a><\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>Colored top-m-to-random shuffles (2026)<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">Lightning talk at the <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/scgp.stonybrook.edu\/archives\/45985\" target=\"_blank\" rel=\"noopener\">4th Simons Math Summer Workshop: Algebraic Methods in Probability<\/a> (July 2026)<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>The Magic of Colored Top-m-to-Random Shuffles (2026)<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">USC Graduate Student Colloquium<\/span><span class=\"ir-resources\" style=\"display: block; margin-top: 8px; font-size: 14px; line-height: 1.85; font-weight: 400;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/www.youtube.com\/watch?v=r1XBMxZz9oA\" target=\"_blank\" rel=\"noopener\">Presentation Recording<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2026\/05\/Notes_colored_top_m_to_random_shuffles.pdf\" target=\"_blank\" rel=\"noopener\">Companion Notes<\/a><\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>The Math Teaching Atlas (2026)<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">USC Math Education Seminar, <em>Great Teaching Leaves Trails<\/em> (March 23), and MAA MathFest poster, <em>Trails, Anchors, and Compass in Action<\/em> (August 7)<\/span><span class=\"ir-resources\" style=\"display: block; margin-top: 8px; font-size: 14px; line-height: 1.85; font-weight: 400;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/www.youtube.com\/watch?v=zDtwzoaw-7Q&amp;t=1844s\" target=\"_blank\" rel=\"noopener\">Presentation Recording<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/arxiv.org\/pdf\/2504.04313\" target=\"_blank\" rel=\"noopener\">Paper<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1aQBE6ukJ7_NbZVKiZXzGIusFz6rS9g0F\/view?usp=drivesdk\" target=\"_blank\" rel=\"noopener\">Poster<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1g85Gms3_-UOy5pzz2hwbrA6LSmlwugOT\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Flyer<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1k6-jM12rhLFDgW8MBxb8i4RmpaCTpQCo\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Handout<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1ANG8rYkzAgRguB2QlV-fNeuBJbkOHpf5\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Notes<\/a><\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>The Dual Burnside Process<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">USC Graduate Colloquium (October 14, 2025).<\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/calendar.usc.edu\/event\/math-graduate-colloquium-zeta-primes-zeros-and-beyond\" target=\"_blank\" rel=\"noopener\">Zeta: Primes, Zeros, and Beyond<\/a><\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">(March 25, 2025)<\/span><span class=\"ir-resources\" style=\"display: block; margin-top: 8px; font-size: 14px; line-height: 1.85; font-weight: 400;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/youtu.be\/J207N3clCEY?si=L-yZxPxXkn180JeU\" target=\"_blank\" rel=\"noopener\">Presentation Recording<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1sM7U3E_UqWfdarkRqPriN62wo3Ol0xgq\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Flyer<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1YxHe7jGOJpjsTi3SybuR_Ai7S_Ne7tua\/view?usp=drivesdk\" target=\"_blank\" rel=\"noopener\">Handout<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1RHaS-l4tqfTyPWApYuaxFBq47HJgPv8u\/view?usp=drivesdk\" target=\"_blank\" rel=\"noopener\">Notes<\/a><\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>Exploring Leray\u2019s Formulation of the Navier-Stokes Equations<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">(2024)<\/span><span class=\"ir-resources\" style=\"display: block; margin-top: 8px; font-size: 14px; line-height: 1.85; font-weight: 400;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/www.youtube.com\/watch?v=RawqdzQiHOw&amp;t=183s\" target=\"_blank\" rel=\"noopener\">Presentation Recording<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/18WozjFdNPHF2oqMJqHUplke2d9IGnBOS\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Notes<\/a><\/span><\/p>\n<p class=\"ir-entry\" style=\"margin: 0 0 25px; padding: 0 14px; text-align: center;\"><span class=\"ir-entry-title\" style=\"display: block; margin: 0; color: #30383b; font-size: 17px; line-height: 1.65; font-weight: 400;\"><em>Weak convergence theorems in the Theory of Probability<\/em><\/span><span class=\"ir-meta\" style=\"display: block; margin-top: 5px; color: #59656c; font-size: 15px; line-height: 1.65; font-weight: 400;\">(2022)<\/span><span class=\"ir-resources\" style=\"display: block; margin-top: 8px; font-size: 14px; line-height: 1.85; font-weight: 400;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/youtu.be\/y-8PcqOTpPE?si=EeE7pneWxW58bKhf\" target=\"_blank\" rel=\"noopener\">Presentation Recording<\/a> \u00b7 <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1Ta7Ps7NN0XAbmqUUrD1USyIIyy7zusId\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Notes<\/a><\/span><\/p>\n<\/section>\n<section id=\"coursework-notes\" class=\"ir-section\" style=\"margin-top: 46px;\" aria-labelledby=\"coursework-notes-title\">\n<div class=\"ir-section-header\" style=\"padding-bottom: 13px; margin-bottom: 25px; border-bottom: 1px solid #ccdce2;\">\n<h2 id=\"coursework-notes-title\" style=\"margin: 0; padding: 0; color: #273b44; font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; font-size: 21px; line-height: 1.4; font-weight: 600; letter-spacing: 0; text-transform: none;\">Selected coursework notes<\/h2>\n<p><a class=\"ir-back\" style=\"color: #627880; font-size: 12px; line-height: 1.5; font-weight: 400; text-decoration: none; white-space: nowrap;\" href=\"#research-contents\" aria-label=\"Back to table of contents\">\u2191 Contents<\/a><\/p>\n<\/div>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/drive\/folders\/1jwByLlqa2nTuYV5AGoS77xXdHornvhKo?usp=sharing\" target=\"_blank\" rel=\"noopener\">Math 500: Ivan&#8217;s Colloquia Notes and Reports<\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1Uvx4UXvL36joJMxfNur65WSxRsq2YR49\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Math 520: Ivan&#8217;s Solutions to Some Exercises from Ahlfors&#8217;s <em>Complex Analysis<\/em><\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/drive\/folders\/1qu1G8nFIAH6mv1aeE0_ePBBqr64lmPeQ?usp=sharing\" target=\"_blank\" rel=\"noopener\">Math 532: Ivan&#8217;s Solutions to Some Exercises from Aigner&#8217;s <em>A Course in Enumeration<\/em><\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/drive\/folders\/1-5cfI0y16zSRL7JNDh1Jy7vQA1HBM5qf?usp=share_link\" target=\"_blank\" rel=\"noopener\">Math 541: Ivan&#8217;s Solutions to Exercises in Heilman&#8217;s Lecture Notes<\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/imathman.medium.com\/thoughts-on-what-good-math-tas-should-be-like-e1c32712e78c\" target=\"_blank\" rel=\"noopener\">Math 595: Ivan&#8217;s Thoughts on Teaching<\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1ogJf7aNP6WLg2xGhamUWlMX6zCHczCLJ\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Math 610: Ivan&#8217;s Selected Homework Solutions<\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/drive\/folders\/1N1fA62pChPYFb1b1lfnLWckTdrqxFrmN?usp=sharing\" target=\"_blank\" rel=\"noopener\">Math 641: Ivan&#8217;s Solutions to Selected Homework Problems<\/a><\/p>\n<\/section>\n<section id=\"graduate-courses\" class=\"ir-section\" style=\"margin-top: 0;\" aria-label=\"Graduate coursework at USC\">\n<details style=\"margin: 30px 0; border: 1px solid #dce6e2; border-radius: 10px; padding: 16px 18px;\">\n<summary style=\"cursor: pointer; font-weight: bold; font-size: 17px;\">Graduate coursework at USC<\/summary>\n<p style=\"margin: 14px 0;\"><a href=\"https:\/\/catalogue.usc.edu\/preview_entity.php?catoid=16&amp;ent_oid=3436&amp;hl\" target=\"_blank\" rel=\"noopener\">USC graduate mathematics course catalogue<\/a><\/p>\n<p style=\"text-align: center; margin: 0 0 18px;\">Math 500 (Graduate Colloquium) [Spring 2023];<br \/>\n505a (Applied Probability) [Fall 2024];<br \/>\n507a, b (Theory of Probability) [Fall 2022, Spring 2024];<br \/>\n510a, b (Algebra) [Fall 2020, Spring 2021];<br \/>\n514 (Algebraic Geometry) [Spring 2025];<br \/>\n520 (Complex Analysis) [Spring 2021];<br \/>\n525a, b (Real Analysis) [Fall 2020, Spring 2021];<br \/>\n532 (Combinatorial Analysis) [Fall 2022];<br \/>\n535a (Differential Geometry) [Spring 2021];<br \/>\n540 (Topology) [Fall 2020];<br \/>\n541a (Introduction to Mathematical Statistics) [Spring 2023];<br \/>\n555a, b (Partial Differential Equations) [Fall 2021, Spring 2022];<br \/>\n565a (Ordinary Differential Equations) [audited, Spring 2022];<br \/>\n580 (Introduction to Functional Analysis) [Fall 2023];<br \/>\n590 (Directed Research) [Summer 2024], [Fall 2024, with Prof. <a href=\"https:\/\/sites.google.com\/view\/edimitrov\/\" target=\"_blank\" rel=\"noopener\">Evgeni Dimitrov<\/a> and Prof. <a href=\"https:\/\/julianchaidez.net\/\" target=\"_blank\" rel=\"noopener\">Julian Chaidez<\/a>], [Summer 2025];<br \/>\n594a, b, z (Master\u2019s Thesis) [Fall 2021, Spring 2022];<br \/>\n595 (Practicum in Teaching the Liberal Arts: Mathematics) [Fall 2022];<br \/>\n599 (Special Topics) [Fall 2025];<br \/>\n605 (Topics in Probability) [Fall 2023];<br \/>\n610 (Topics in Algebra) [Summer 2023];<br \/>\n633 (Topics in Combinatorics; topic: Combinatorics and Markov chains) [Fall 2026, in progress];<br \/>\n641 (Topics in Topology) [Spring 2023];<br \/>\n655 (Topics in Differential Equations) [Spring 2024];<br \/>\n790 (Research) [Spring 2025, with Prof. <a href=\"https:\/\/dornsife.usc.edu\/aravind-asok\/\" target=\"_blank\" rel=\"noopener\">Aravind Asok<\/a>];<br \/>\n794a, b, c (Doctoral Dissertation) [Fall 2025], [Spring 2026], [Fall 2026, in progress].<\/p>\n<\/details>\n<\/section>\n<section id=\"other-work\" class=\"ir-section\" style=\"margin-top: 46px;\" aria-labelledby=\"other-work-title\">\n<div class=\"ir-section-header\" style=\"padding-bottom: 13px; margin-bottom: 25px; border-bottom: 1px solid #ccdce2;\">\n<h2 id=\"other-work-title\" style=\"margin: 0; padding: 0; color: #273b44; font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; font-size: 21px; line-height: 1.4; font-weight: 600; letter-spacing: 0; text-transform: none;\">Other fun work<\/h2>\n<p><a class=\"ir-back\" style=\"color: #627880; font-size: 12px; line-height: 1.5; font-weight: 400; text-decoration: none; white-space: nowrap;\" href=\"#research-contents\" aria-label=\"Back to table of contents\">\u2191 Contents<\/a><\/p>\n<\/div>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1tVFB1-cPADu2ASWtvQEMS2JvDRH1BHmP\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">Two Methods (Topology &amp; Geometry) to Prove the Hairy Ball Theorem<\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1Fd1Pn9NjyiS_kelYn3tiYWHclpUpq4BV\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">An Easy Introduction to the Motivic Zeta Function for A^l and P^l<\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/file\/d\/1I5emuDK6hkaLS20ZIh4_-DrESMJHTO4Z\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\">An interesting extension of a basic calculus problem<\/a><\/p>\n<p style=\"margin: 0 0 19px; padding: 0 12px; text-align: center; font-size: 16px; line-height: 1.7;\"><a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/drive.google.com\/drive\/folders\/11OoUGIY4bt3nuFXNBfHC9zfhRzf2qLMC?usp=sharing\" target=\"_blank\" rel=\"noopener\">DRP Notes<\/a> (<em>Mathematical Statistics with Applications<\/em>, 7th edition)<\/p>\n<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-750 aligncenter\" style=\"display: block; width: 100%; max-width: 100%; height: auto; margin: 38px 0 16px; border-radius: 10px;\" src=\"https:\/\/dornsife.usc.edu\/zhanhu\/wp-content\/uploads\/sites\/215\/2023\/12\/IMG_5767-scaled.jpeg\" alt=\"A view of the ocean and shoreline along the Los Angeles coast\" width=\"2560\" height=\"1920\" srcset=\"https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2023\/12\/IMG_5767-scaled.jpeg 2560w, https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2023\/12\/IMG_5767-300x225.jpeg 300w, https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2023\/12\/IMG_5767-1024x768.jpeg 1024w, https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2023\/12\/IMG_5767-768x576.jpeg 768w, https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2023\/12\/IMG_5767-1536x1152.jpeg 1536w, https:\/\/dornsife.usc.edu\/ivan\/wp-content\/uploads\/sites\/215\/2023\/12\/IMG_5767-2048x1536.jpeg 2048w\" sizes=\"(max-width: 2560px) 100vw, 2560px\" \/><\/p>\n<p style=\"margin: 0; color: #59656c; font-size: 15px; line-height: 1.8; text-align: left;\"><em>Note: This picture was taken along the Los Angeles coast in August 2022. I&#8217;ve placed it here because the view is incredibly beautiful, with a hint of mysterious and surreal atmosphere. During that trip, I was so captivated by the seaside scenery that I ended up writing two poems titled &#8220;Seashore Duet&#8221; (which can be found on <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"https:\/\/dornsife.usc.edu\/ivan\/2022-2\/\" target=\"_self\">the 2022 poetry page<\/a>) to immortalize my memories. In August 2023, exactly one year later and just before the semester started, I revisited the same place since I was feeling nostalgic. I left another poem there, titled &#8220;Coastal Symphony&#8221; (which can be found on <a style=\"color: #0b5f84; font-weight: 400; text-decoration: underline; text-decoration-thickness: 1px; text-underline-offset: 3px;\" href=\"\/ivan\/2023-2\/\" target=\"_self\">the 2023 poetry page<\/a>).<\/em><\/p>\n<section id=\"research-statement\" class=\"ir-section\" style=\"margin-top: 46px;\" aria-labelledby=\"research-statement-title\">\n<div class=\"ir-section-header\" style=\"padding-bottom: 13px; margin-bottom: 25px; border-bottom: 1px solid #ccdce2;\">\n<h2 id=\"research-statement-title\" style=\"margin: 0; padding: 0; color: #273b44; font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; font-size: 21px; line-height: 1.4; font-weight: 600; letter-spacing: 0; text-transform: none;\">Research statement<\/h2>\n<p><a class=\"ir-back\" style=\"color: #627880; font-size: 12px; line-height: 1.5; font-weight: 400; text-decoration: none; white-space: nowrap;\" href=\"#research-contents\" aria-label=\"Back to table of contents\">\u2191 Contents<\/a><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" src=\"https:\/\/drive.google.com\/file\/d\/1UfbTBDfAldCjjlXvI1z-Ym2RM1CRXH82\/preview\" width=\"100%\" height=\"480\" title=\"Research statement\"><\/iframe><br \/>\n<\/section>\n<\/div>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n\n\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p><em>Last update: Oct 31, 2026<\/em><\/p>\n<p><a href=\"https:\/\/dornsife.usc.edu\/ivan\" target=\"_self\"><em>Back to my homepage<\/em><\/a><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":390,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-208","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Research - Ivan Z. 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