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1 Jan 2019: Advanced AnalysisLectures by Denis Serre. Notes by Alexis Marchand. ENS de LyonS1 2018-2019. M1 course. Contents1 Topological vector spaces 2. 1.1 Generalities. 21.2 Completeness. 3. 2 Convexity 42.1 Locally convex topological vector spaces. 52.2

4 Jan 2019: Advanced GeometryLectures by Jean-Claude Sikorav. Notes by Alexis Marchand. ENS de LyonS1 2018-2019. M1 course. Contents1 Differentiable manifolds 2. 1.1 Generalities. 21.2 Submanifolds of RN. 3. 2 Differentiable maps and tangent bundle 42.1

6 Jan 2019: 24. 1. 5 Integral extensions 255.1 Integral elements. 255.2 Finiteness of invariants.

10 Jan 2019: 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

10 Jan 2019: 24. Exercise 10.4. Repeat the counter-example of Exercise 10.2. Take n = 2,.

10 Jan 2019: 1. 9 Gaussian integration 22. 10 Distance and compact sets 24. ... 24. Let us write τ(E,F ) = infyE d(y,F). Exercise 10.4.

22 Feb 2019: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4.

11 Mar 2019: We note that by Lemma 2.24 each component grλ G is an abelian group. ... Since Gt/Gt+ iscentral in G/Gt+ (Lemma 2.24) we obtain. gλµGt+ = gλgµGt+ = hGt+.

23 Mar 2019: Notre Dame Journal of Formal Logic55 (1):11-24 (2014). [2] Crabbé, Marcel “Stratification and Cut-elimination”.

4 Apr 2019: 24. 8 Cyclotomic fields 27. These are Jack Thorne’s notes for the Part II Number Fields course, lectured in Lent term 2019 at theUniversity of Cambridge.

12 Apr 2019: Riemann SurfacesLectures by François BrunaultNotes by Alexis Marchand. ENS de LyonS2 2018-2019. M1 course. Contents1 Elliptic functions and complex tori 2. 1.1 Lattices and complex tori. 21.2 Elliptic functions. 21.3 The Weierstraß -function. 31.4

17 Apr 2019: Number TheoryLectures by Amaury ThuillierNotes by Alexis Marchand. ENS de LyonS2 2018-2019. M1 course. Contents1 Number fields and rings of integers 1. 1.1 Algebraic and integral numbers. 11.2 Number fields. 21.3 Traces, norms and discriminants.

1 May 2019: 8.2. Pushforward along an open embedding. We now recall from [8] thatweak holonomicity is generally not stable under pushforward either.For this, recall from [24, Definition 13.1.1] that

8 May 2019: Grants held. 2005-2008 EPSRC Postdoctoral Fellowship Grant No. EP/C527348/1. Teaching. As an Affliated Lecturer I give 24 lectures a year for the Cambridge University Faculty of Mathematics inaddition

15 May 2019: 24 (2015), 480--485 (with I. B. Leader) Monochromatic infinite sumsets, submitted (with P.

16 May 2019: Réponses :1.ni=0. nj=0 i. 2j3 = n3(n1)3(2n1). 24. 2.ni=1. i3j=i 2j2i = 2n(n 1). ... Exercice II.3.24 (? ). Soit f : R R vérifiant f(x) = x axb o0(xb), avec a ]0, [,b ]1, [. On définit la suite (un)nN par u0 R+ et n

25 Jun 2019: D. Sorbonne, 1930; visited Berlin, Ham-. burg, Göttingen 1931; killed climbing.10 Kurt Gödel, 1906–1978; in Vienna from ’24 (Ph.D. ... and Gödel.24 Black’s review [Bl1] of both [HiB2] and a 1938 survey paper [G3] of Gentzen.

9 Aug 2019: 23. 5 Conclusion: at the junction of two paths 24. References 25.

5 Oct 2019: Most. of the courses are 24 lectures long and delivered at the rate of 3 a week,but some are 16 lectures long and delivered at the rate of 2 a

6 Oct 2019: 24. Questions? 24. Which moduli spaces? Homological stability. Stable cohomology. Beyond stable homology.

15 Oct 2019: Example sheet 2 (updated 24 November 2004). ... Example sheet 3 (updated 24 November 2004).

27 Oct 2019: Lemma 3.24. The sphere S = colim Sn is contractible. Sketch proof.

30 Oct 2019: g]| 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

31 Oct 2019: g]| 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

2 Nov 2019: π2. 3. (1 24. n=1. σ1(n)qn. ). Explain why G2(z) is not a modular form of weight 2.

2 Nov 2019: This provesthe uniqueness, i.e. that if d exists then it must be expressed by (1.24) in local coordinates. ... So let d′ denote the exterior differentiation constructed asin (1.24), but using different choice of local coordinates.

3 Nov 2019: Date: October 24, 2019.1. In Section 2, we begin by proving the analogue of the theorem of Poonen and Voloch forhypersurfaces in products of projective spaces:.

8 Nov 2019: Theorem 2.24. If X is a path-connected, locally simply connected2 topolog-ical space, then there exists a universal cover p X̃ X. ... 24. Example 2.28. Example 2.20 tells us that π1(S1, 1) Z.

11 Nov 2019: 24 alexei kovalev. with the local complex coordinate z = z2/z1 on U1, and ζ = z1/z2 on U2, and ζ = 1/z whenz 6= 0.

18 Nov 2019: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.

25 Nov 2019: November 24, 2019. 2. Chapter 1. Lebesgue spaces. This chapter is devoted to the derivation of fundamental properties of Lebesgue spaces Lp(Rd).After recalling classical inequalities (Hölder, Minkowski and Young), ... 24. and hecne X|fn(x)|pdµ(x). (sup.

28 Nov 2019: 4. Let E2(z) = 1 24. n=1 σ1(n)qn = (3/π2)G2(z) as in sheet 2, Q8.

2 Dec 2019: PROBABILITY AND MEASURE, LECTURES NOTES. MICHAELMAS 2019-2020, E. BREUILLARD. Lecture 1. 0. Plan for the course. Useful material for the course include:. ‚ Lecture notes by James Norris available on the course’s website.‚ the course syllabus

24 Dec 2019: These arecopies of X0(m) for m = 19, 20, 21, 24 and 32. ... Proof. This is [AR, Theorem 24.1]. The proof works by analysing the exact se-.