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Paul Russell's Papers and Preprints
https://www.dpmms.cam.ac.uk/~par31/preprints/15 May 2019: 24 (2015), 480--485 (with I. B. Leader) Monochromatic infinite sumsets, submitted (with P. -
NON-TRIVIALITY OF TORSION UNIVERSAL CHARACTERISTIC CLASSES OF…
https://www.dpmms.cam.ac.uk/~or257/Torsion.pdf1 Oct 2012: Oscar Randal-Williams, Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, United. -
Part IID Differential Geometry (Michaelmas 2011) A.G. Kovalev…
https://www.dpmms.cam.ac.uk/~agk22/chi.pdf23 Nov 2011: 1. Triangulating a ‘topological pretzel’: χ = 24 44 18 = 2, g = 2. -
Publications | Department of Pure Mathematics and Mathematical…
https://www.dpmms.cam.ac.uk/publications?page=11213 Jul 2024: 2007). 24,. 159. (doi: 10.3934/dcds.2009.24.159). Statistical Dependence in Biological Sequences. HM Aktulga, I Kontoyiannis, LA Lyznik, L Szpankowski, AY Grama, W Szpankowski. – ... 2007). 24,. 6201. (doi: 10.1088/0264-9381/24/24/004). Representations -
IA Groups - Example Sheet 3 Michaelmas 2022 rdc26@cam.ac.uk ...
https://www.dpmms.cam.ac.uk/study/IA/Groups/2022-2023/gps322.pdf8 Nov 2022: a) Let H 6 Cn. Identify the quotient Cn/H. (b) Show that N = {e, (12)(34), (13)(24), (14)(23)} is a normal subgroup of S4. -
Profinite Groups, Exercise Sheet 2 Lent 2021 [Key questions ...
https://www.dpmms.cam.ac.uk/~grw46/ProfinitGroups_Exs2.pdf19 Jan 2021: 24, x. 14 x1x4 = x. 21. 〉has no finite quotients other than the trivial group. -
Part III Analysis of PDE: Rough syllabus Claude Warnick ...
https://www.dpmms.cam.ac.uk/~cmw50/resources/PartIIIPDE/PDESyllabus.pdf15 Oct 2021: Part III Analysis of PDE: Rough syllabus. Claude Warnick. April 24, 2019. -
N-Congruences Between Quadratic Twists of Elliptic Curves
https://www.dpmms.cam.ac.uk/~stf32/slides/qttslides_yrant.pdf7 Sep 2021: quadratic twist if and only ifeither N 12, N 24 is even, N = 28 or N = 36. -
Pierre RAPHAËL Herchel Smith Professor of Pure MathematicsDepartment …
https://www.dpmms.cam.ac.uk/files/raphael/cv-complet-2022.pdf25 Jan 2022: 163 (2014), no. 2, 369–431. [24] Raphaël, P.; Schweyer, R., Stable blow up dynamics for the 1-corotational energy critical harmonic heat flow,Comm. ... Vlasov-Poisson system, Ann. Inst. H. Poincaré Anal. Non Lind́eaire 24 (2007), no. -
GLOBAL PERTURBATIVE CLASSICAL SOLUTIONS OF THE BOLTZMANN EQUATION…
https://www.dpmms.cam.ac.uk/~md384/Boltzmann-long-range.pdf14 Feb 2017: Math. Soc. 24 (2011), no. 3, 771–847. [4] Alexandre, R.; Morimoto, Y.; Ukai, S.; Xu, C.-J.; Yang, T. -
Example sheet 3, Galois Theory (Michaelmas 2022)…
https://www.dpmms.cam.ac.uk/study/II/Galois/2022-2023/ex3.pdf22 Nov 2022: 1. (i) What are the transitive subgroups of S4? Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.(ii) Let -
IA Groups - Example Sheet 3 Michaelmas 2021 rdc26@cam.ac.uk ...
https://www.dpmms.cam.ac.uk/study/IA/Groups/2021-2022/gps321.pdf8 Nov 2021: a) Let H 6 Cn. Identify the quotient Cn/H. (b) Show that N = {e, (12)(34), (13)(24), (14)(23)} is a normal subgroup of S4. -
Publications | Department of Pure Mathematics and Mathematical…
https://www.dpmms.cam.ac.uk/publications?page=8913 Jul 2024: V Chulaevsky, AB de Monvel, Y Suhov. – Nonlinearity. (2011). 24,. ... 1451. (doi: 10.1088/0951-7715/24/5/004). An isoperimetric inequality for the Wiener sausage. Y Peres, P Sousi. – -
Diffeomorphisms of discs
https://www.dpmms.cam.ac.uk/~or257/slides/Copenhagen2020.pdf8 Sep 2020: 54. 56. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 ... 44. 46. 48. 50. 52. 54. 56. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 -
Mich. 2018 GRAPH THEORY—EXAMPLES 3 PAR 1(a) For which ...
https://www.dpmms.cam.ac.uk/study/II/Graphs/2018-2019/18sheet3.pdf5 Nov 2018: 1) = 1. There must be a 24-path from x2 to x4 or we can make some colour swap and colour v. ... 1) = 1. There must be a 23-path from x2 to x3 and a 24-path from x2 to x4 or we can make some colour swap and. -
Lent Term 2024 O. Randal-Williams IB Groups, Rings, and ...
https://www.dpmms.cam.ac.uk/study/IB/GroupsRings%2BModules/2023-2024/Sheet3.pdf15 Jan 2024: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4. -
Mich. 2023 SJW Representation Theory — Examples Sheet 2 ...
https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2023-2024/2023ex2.pdf25 Oct 2023: 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. -
Example sheet 3, Galois Theory (Michaelmas 2005)…
https://www.dpmms.cam.ac.uk/study/II/Galois/ex3.pdf12 Nov 2005: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.(ii) Let f Z[X] be monic and separable of degree -
Modular forms and L-functions (Michaelmas 2019) — example sheet ...
https://www.dpmms.cam.ac.uk/~ajs1005/modular/ex-sheet-2-2019.pdf2 Nov 2019: π2. 3. (1 24. n=1. σ1(n)qn. ). Explain why G2(z) is not a modular form of weight 2. -
Pattern Matching and Lossy Data Compression on Random Fields ...
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/RFS2.pdf5 Jun 2020: This. 2. result generalizes the corresponding bound of Steinberg and Gutman [24] for one-dimensionalsources. ... 24] Y. Steinberg and M. Gutman. An algorithm for source coding subject to a fidelity criterion,based upon string matching. -
Elliptic Curves and Modularity Jack A. Thorne Abstract We ...
https://www.dpmms.cam.ac.uk/~jat58/EMS.pdf29 Sep 2023: 24, 14].). Our first goal in this article is to state the a version of this modularity conjecture forelliptic curves over a general number field K in as down to earth ... 24] F. Grunewald, H. Helling, J. Mennicke, SL2 over complex quadratic number fields. -
Modular forms and L-functions (Michaelmas 2019) — example sheet ...
https://www.dpmms.cam.ac.uk/~ajs1005/modular/ex-sheet-4-2019.pdf28 Nov 2019: 4. Let E2(z) = 1 24. n=1 σ1(n)qn = (3/π2)G2(z) as in sheet 2, Q8. -
Lossless Compression with Moderate Error Probability
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/MDP.pdf5 Jun 2020: Previous work along theselines has been described in [24]–[29]. These studies reportthat error probability vanishes sub-exponentially fast, and theycharacterize the rate of this decay. ... 24] J. Chen, D.-k. He, A. Jagmohan and L. A. Lastras-Montaño, -
Estimating the Entropy Rate of Spike Trains Yun GaoDiv. ...
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/spikes-CISS.pdf5 Jun 2020: In-form. Theory, 24:530–536, 1978. 3. -
The ODE Method and Spectral Theory of Markov Operators ...
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/hkm.pdf5 Jun 2020: Sadhana, 24(4-5):425{452, 1999. Chance as necessity. 8. V.S. Borkar and S.P. ... Sadhana, 24(4-5):369{423, 1999. Chance as necessity. 16. S.V. Hanly and D. -
Example sheet 3, Galois Theory, 2021 1. Let M/K ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2021-2022/ex3_2021.pdf15 Oct 2021: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}. -
Geometry-of-numbers over number fields and the density of ADEfamilies …
https://www.dpmms.cam.ac.uk/~mo512/nf.pdf23 May 2024: 1. 5.1 Averaging and reductions. 21. 5.2 Slicing. 24. 5.3 Congruence conditions. -
Spaces of manifolds
https://www.dpmms.cam.ac.uk/~or257/slides/Princeton2022.pdf13 Apr 2022: 40. 42. 44. 46. 48. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 -
The Ward Correspondence and StationaryAxisymmetric Spacetimes…
https://www.dpmms.cam.ac.uk/~gt306/mp1.pdf16 Jan 2024: where. νabcd =1. 24. det(η)εabcd. The coordinates (w,z,w̃, z̃) are called double null coordinates. ... wγn = z̃γn1 and zγn = w̃γn1. (24). The Birkhoff factorization F = f̃1f is given by4. -
Lent Term 2016 O. Randal-Williams IB Groups, Rings, and ...
https://www.dpmms.cam.ac.uk/~or257/teaching/IBGRM/Sheet3.pdf15 Feb 2016: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4. -
Ek-algebras and homological stability
https://www.dpmms.cam.ac.uk/~or257/slides/eCHT.pdf16 Jan 2020: Figure 1: Hd(Γg,1, Γg1,1; Q);? means unknown,? means not zero. Non-zero groups: use results of Faber, Kontsevich, Morita.24. -
Hamilton Paths in Certain Arithmetic Graphs Paul A. Russell∗† ...
https://www.dpmms.cam.ac.uk/~par31/preprints/hamilton.pdf30 Jan 2005: But what we need is simply a Hamilton path from 0to 54 in G3 [[0, 21] {24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60}], for which ... 0, 3, 1, 4, 7, 10, 13, 16, 19, 57, 60, 20, 17, 14, 11, 8, 5, 2, 6, 9, 12, 15, 18, 21,24, 27, 30, 33, 36, 39, 42, -
MATHEMATICAL TRIPOS PART II (2022–2023)CODING AND CRYPTOGRAPHY…
https://www.dpmms.cam.ac.uk/study/II/Coding/2022-2023/CC3-20.pdf11 Jan 2023: Colourtransmission requires three times the amount of data than Mariner 9 needed, so a Golay (24,12,8) code wasused. -
filtersurprise.dvi
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/filtering.pdf5 Jun 2020: Filtering: The Case for “Noisier” Data. B. Lucena I. Kontoyiannis†. August 24, 2005. -
talk.dvi
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/mdl-msri.pdf5 Jun 2020: 24. Step 7. Applications: Preprocessing in VQ Design. Remarks. So far, everything based on “measures (random) codes” correspondencePractical implications? -
talk.dvi
https://www.dpmms.cam.ac.uk/~ik355/AWMCMC/AWMCMC_talks/IK.pdf6 Jun 2020: Which Spectrum? I. KontoyiannisAthens U. of Econ & Business. joint work with S.P. Meyn. University of Illinois/Urbana-Champaign. Athens Workshop on MCMC Convergence and Estimation. 1. Outline. Motivation. In general:Geometric ergodicity spectral gap -
vt06final.dvi
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/vt.pdf5 Jun 2020: Γn(F) will be to obtain a bound on the deviationprobability (24) with an appropriately chosen shadowfunction D. ... Probab., 24(2):916–931, 1996. [17] P.W. Glynn and D. Ormoneit. Hoeffding’s inequality foruniformly ergodic Markov chains. -
The Complexity and Entropy of Literary Styles� I. Kontoyiannisy ...
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/english.pdf5 Jun 2020: In his landmark 1948 paper, [24], Shannon dened the entropy and the redundancy of a language,. ... 24] C.E. Shannon. A mathematical theory of communication. Bell System Technical J., 27:379{. -
Example sheet 3, Galois Theory (Michaelmas 2013)…
https://www.dpmms.cam.ac.uk/~ajs1005/gal2d/ex-sheet3.pdf17 Nov 2013: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.(ii) Let f Z[X] be monic and separable of degree -
Michaelmas Term 2023 T.A. Fisher Galois Theory: Example Sheet ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2023-2024/galois_theory-23-3.pdf7 Nov 2023: Find a monic polynomial over Z ofdegree 4 whose Galois group is V = {id, (12)(34), (13)(24), (14)(23)}.(ii) Let f Z[X] be monic and separable of degree -
Simulated Convergence Rates with Application to anIntractable…
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/CAMSAP.pdf5 Jun 2020: the latter in terms ofthe commonly used divergence measures, such as Kullback-Leibler divergence (KLD) and α-divergence, see [24]. ... dissertation, Kaiserslautern University of Technology, 2014. [24] Minka, T., “Divergence measures and message passing -
MA4K5: Introduction to Mathematical Relativity Dr. Claude Warnick…
https://www.dpmms.cam.ac.uk/~cmw50/resources/MA4K5/MA4K5Intro.pdf15 Oct 2021: 24. 2.1.1 Examples of pseudo-Riemannian manifolds. 262.1.2 Causal geometry for Lorentzian manifolds. -
IA Groups - Example Sheet 3 Michaelmas 2020 ak467@cam.ac.uk ...
https://www.dpmms.cam.ac.uk/study/IA/Groups/2020-2021/Groups_Sheet3.pdf11 Nov 2020: b) Show that N = {e, (12)(34), (13)(24), (14)(23)} is a normal subgroup of S4. -
Mich. 2022 SJW Representation Theory — Examples Sheet 2 ...
https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2022-2023/2022ex2.pdf27 Oct 2022: 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. -
Lent Term 2018 O. Randal-Williams IB Groups, Rings, and ...
https://www.dpmms.cam.ac.uk/~or257/teaching/IBGRM/2018/Sheet3.pdf23 Feb 2018: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4. -
Example sheet 3, Galois Theory, 2019 1. Let M/K ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2019-2020/ex3_2019.pdf18 Nov 2019: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}. -
PubTeX output 1999.09.27:1044
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/lossyJ.pdf5 Jun 2020: for all. (24)Then, by the duality relationship (15) and the fact that. ... Inform.Theory, vol. 43, pp. 1439–1451, Sept. 1997. [24] H. Morita and K. -
ON PAIRS OF 17-CONGRUENT ELLIPTIC CURVES T.A. FISHER Abstract. ...
https://www.dpmms.cam.ac.uk/~taf1000/papers/congr17.pdf4 Jun 2021: 56 176 148 68 160 140 36 52 24 24 8 4. ... 36 72 96 96 12 24 36 12 0 24 24 12. -
Analysis of Partial Differential Equations Example sheet 3 (Chapter…
https://www.dpmms.cam.ac.uk/~md384/example_sheet_PDE_3-v3.pdf11 Nov 2016: 24). (15.a) Using an existence result from the theory of ODEs, show that for each n N there exists a uniquefunction un(t) of the form (23) satisfying (24).[Hint: ... Show that the limit function is indeed a weak solution of (20) inthe sense of (22) by -
E-algebras and general linear groups
https://www.dpmms.cam.ac.uk/~or257/slides/Regensburg2020.pdf13 Apr 2021: E-cells and general linear groups of finite fields.arXiv:1810.11931. 24. The Steinberg module.
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