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Title: Lecture Notes | Gilles Castel

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Description: Website of Gilles Castel

Open Graph Description: Website of Gilles Castel

X Description: Website of Gilles Castel

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gilles@castel.dev

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Domain: castel.dev

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twitter:creatorGilles Castel

Links:

Gilles Castelhttps://castel.dev/
Githubhttps://github.com/gillescastel
Twitterhttps://twitter.com/gilles_castel
Quorahttps://www.quora.com/profile/Gilles-Castel-1
YouTubehttps://www.youtube.com/channel/UCbW6-rTEn6nPj56K_9dLozQ
RSShttps://castel.dev/rss.xml
Articleshttps://castel.dev/
Lecture Noteshttps://castel.dev/notes
Talkshttps://castel.dev/talks
Contacthttps://castel.dev/contact
Githubhttps://github.com/gillescastel/lecture-notes
G0A84AEhttps://onderwijsaanbod.kuleuven.be/syllabi/e/G0A84AE.htm
Lecture notesMunkres: Fundamental groups, covering spaces, Seifert-Van Kampen, classification of covering spaces. Vick: Singular homology, Mayer-Vietoris, maps from spheres to spheres, hairy ball theorem, ham sandwich theorem, etc.https://drive.google.com/uc?export=download&id=1bJPrXTVYBLFrztq334IoX9GtEfvEYPYu
G0B08AEhttps://onderwijsaanbod.kuleuven.be/syllabi/e/G0B08AE.htm
Lecture notesDifferentiable manifolds, tangent vectors, vector fields, bundles, differential forms and integration, exterior derivative and Stokes theorem, de Rham cohomology, foliations, Lie groups and Lie algebrashttps://drive.google.com/uc?export=download&id=1Ja6Zl-smsejKgS7h6LhRGBblCapQcWbj
G0B03AEhttps://onderwijsaanbod.kuleuven.be/syllabi/e/G0B03AE.htm
Lecture notesBanach, Hilbert spaces, bounded and compact compact operators, Hahn-Banach extension theorem, Baire category, open mapping, closed graph, uniform boundedness, weak topologies, Banach-Alaoglu, Hahn-Banach separation theorem, amenability of groups, Krein-Milmanhttps://drive.google.com/uc?export=download&id=1sbzI2u0ZRhYK9T8p3levkdCnNFv0Z7qr
Takehome IPolar decomposition, Volterra operator, Borel functional calculushttps://drive.google.com/uc?export=download&id=1eM7IAhkD5UtKlR9fbGFJ5t1N4vK35g_I
Takehome IIProperties of bounded operators, weak topology, ... Extreme pointshttps://drive.google.com/uc?export=download&id=1RySb6ckKlrOygmE8-Gn7-FqWe1_2cUjH
G0B11AEhttps://onderwijsaanbod.kuleuven.be/syllabi/e/G0B11AE.htm
Lecture notesSymplectic manifolds, Hamiltonian mechanics, Moser theorem, Darboux theorem, Weinstein lagrangian neighbourhood theorem, Lie groups, Lie group actions, Moment maps, Symplectic reduction, convexity properties of moment mapshttps://drive.google.com/uc?export=download&id=18XNkeFR3jJ69REKhMqdKTlSVGH3a7FVC
G0B05AEhttps://onderwijsaanbod.kuleuven.be/syllabi/e/G0B05AE.htm
Lecture notesRiemann surfaces, Riemann Hurwitz formula, Meromorphic functions on the complex torus, analytical continuation, holomorphic, meromorphic, harmonic differential forms, Hodge decomposition theorem, Abels' theorem, Jacobi inversion theoremhttps://drive.google.com/uc?export=download&id=1kXVklz1lRlQxUGNOye3Ff_ZdU9kNQzMe
G0A85AEhttps://onderwijsaanbod.kuleuven.be/syllabi/e/G0A85AE.htm
Lecture notesRepresentation theory, Character theory, Nilpotent groups, Polycylic groups, Group (co)homology, Group extensionshttps://drive.google.com/uc?export=download&id=12UnmLq4rYlWV5v686-Ng0IMh9YeQyrBZ
G0B12AEhttps://onderwijsaanbod.kuleuven.be/2020/syllabi/v/e/G0B12AE.htm
ReportConnected sums and the Mazur swindlehttps://drive.google.com/uc?export=download&id=1Kc-powlowxxy8cJh11bnJ1MBMfGXbeCS
ReportClassification of vector bundles on sphereshttps://drive.google.com/uc?export=download&id=1dTT7e5OV9EU2CYfF5jwSKUhdm0lU25yX
G0V75AEhttps://onderwijsaanbod.kuleuven.be/2020/syllabi/e/G0V75AE.htm
ReportA classification of topologically stable Poisson structures on a compact oriented surfacehttps://drive.google.com/uc?export=download&id=1N66Cc1TVEL_Xl5g9JGR7im6MRjjet2_Q
G0K97AEhttps://onderwijsaanbod.kuleuven.be/syllabi/e/G0K97AE.htm
Final version (+ LaTeX)Morse Theory: A visual guide from handlebodies to the generalized Poincaré conjecturehttps://github.com/gillescastel/masterthesis
G0N30BNhttps://onderwijsaanbod.kuleuven.be/syllabi/n/G0N30BN.htm
Lecture notesReal numbers, limits, topology of R, (uniform) continuity, sequences of functions, derivatives of functions, series in C, metric spaces, completenesshttps://drive.google.com/uc?export=download&id=19s_im6uKgmo2JysT6Xc5KFVAmPWj9Pzv
Exercise sessionsSolutions to biweekly exercise sessions. Feedback added in greenhttps://drive.google.com/uc?export=download&id=1Bp_5DJkWt96Mni4PCVON6qE5N6aPwTVA
G0N86BNhttps://onderwijsaanbod.kuleuven.be/syllabi/n/G0N86BN.htm
SummaryOverview of all theorems and propositionshttps://drive.google.com/uc?export=download&id=1bv409J367FP94xCQEylemrys6P7WhHY2
X0A43ANhttps://onderwijsaanbod.kuleuven.be/syllabi/n/X0A43AN.htm
Report: Newton fractalsContains some of the most beautiful plots I've ever made. Also covers Bairstowhttps://drive.google.com/uc?export=download&id=1GrsySYoLfLXLGZJ5EP74fQpt4BWxqa5E
Code: Newton fractalsCode accompanying the reporthttps://drive.google.com/uc?export=download&id=1kTot3-ywNYYGaRfqTu-cCrtBy5Ne6jOe
X0C11ANhttps://onderwijsaanbod.kuleuven.be/syllabi/n/X0C11AN.htm
Report: van der Pol equationNumerical analysis of a non-linear ODE via linearization, Euler and Runge-Kutta method using Pythonhttps://drive.google.com/uc?export=download&id=13_ZUAY3jKSfVbs3VtjLcox1-4ppfj-57
X0A65CNhttps://onderwijsaanbod.kuleuven.be/syllabi/n/X0A65CN.htm
Lecture notesDual spaces, bilinear forms, groups, rings, factor rings, polynomial rings, divisbility, field extensions, Wedderburn theorem, Cayley-Hamilton, Jordan decompositionhttps://drive.google.com/uc?export=download&id=13an-mC0aQjc_OcDMk__q1MG-9pbRLNR6
X0D95AEhttps://onderwijsaanbod.kuleuven.be/syllabi/e/X0D95AE.htm
Lecture notesGeneral topology, following Munkreshttps://drive.google.com/uc?export=download&id=1VSHe4Pm866TxpmwzWBtoAr_Ds0Bv54PM
Takehome IOn the Zariski topologyhttps://drive.google.com/uc?export=download&id=1ptE0oj6PEshZWQt2lCSJ2UEZ7ZjWx4-J
Takehome IIProduct topology, Cantor sethttps://drive.google.com/uc?export=download&id=10Li65Nc3_dEbGPk_eP6I5Ou9hfVWy4QZ
Takehome IIICompact versus Lindelöfhttps://drive.google.com/uc?export=download&id=1rtUAyGOsHGKOROfrCVbpnn3R_qeJHgkk
X0C93BNhttps://onderwijsaanbod.kuleuven.be/syllabi/n/X0C93BN.htm
Lecture notesComplex numbers, power series and holomorphic functions, integration, Cauchy theorem, Morera, Schwarz reflection, meromorphic functions, residue theorem, argument and maximum modules principle, homotopies, logarithm, conformal mappings, Riemann mapping theoremhttps://drive.google.com/uc?export=download&id=1PkLRHconRAlG2boVadfpkePuqhhHtNom
X0D42ANhttps://onderwijsaanbod.kuleuven.be/syllabi/n/X0D42AN.htm
ThesisElliptic curves and cryptographyhttps://drive.google.com/uc?export=download&id=1UacpvR0vb3ZoMQZ4crLjkWvTNiNamdUm
PresentationBasics of RSA, elliptic curves and elliptic curve cryptography, algorithm of Lenstrahttps://drive.google.com/uc?export=download&id=16XTZYX3BIahwjUbBLiM7jfZUsRd7bc6W

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