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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Tuesday, 14 May 2024 - 13:30 to 14:30 <br />
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, the blue lecture room in the rear building + ZOOM meeting
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Speaker: Petr Čoupek, Charles University<br />
Title: Iterated integrals and controlled ODEs
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Abstract <br />
<p>The purpose of this non-technical talk is to discuss the role that iterated integrals (an instance of the so-called mapping space signature) play in the theory of ordinary differential equations (ODEs) of the form Y˙ (t) = f(Y (t))X˙ (t) where the path X models the input and the path Y models the output of a physical system whose dynamics is governed by a (non-linear function) f. When X is sufficiently regular (e.g. Lipschitz) function, the solution to the ODE can be, roughly speaking, found as a limit of its iterated integrals. Such regularity is, however, typically not obtained if X is a sample path of a stochastic process (e.g. the Wiener process) and X˙ models the random noise (e.g. the white noise). In the talk, we will discuss why low regularity is a problem, what can be done, and why it is important to understand the algebraical and analytical properties of the iterated integrals (and, more generally, the mapping space signature).</p><p><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);">--------------------------------------------------------------------------------------------------------------------------------------------</span></p><p><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);">ATTENTION: This lecture shall be held on Tuesday instead of Wednesday.</span></p><p><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="ql-font-monospace">We shall open the lecture room + ZOOM at 13.15 for coffee and close the room at 15:00</span></p><p><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="ql-font-monospace">Join Zoom Meeting</span></p><p><a href="https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09" rel="noopener noreferrer" target="_blank" style="color: rgb(0, 0, 204); background-color: rgb(255, 255, 255);" class="ql-font-monospace">https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09</a></p><p><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="ql-font-monospace">MeetingID:99598413922</span></p><p><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="ql-font-monospace">Passcode:Galois</span></p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/16
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Cohomology in algebra, geometry, physics and statistics mailing list <br />
phk_seminar@math.cas.cz <br />
https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
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