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DTSTART;TZID=America/New_York:20260409T160000
DTEND;TZID=America/New_York:20260409T170000
DTSTAMP:20260402T065852
CREATED:20260310T170229Z
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UID:10003917-1775750400-1775754000@cmsa.fas.harvard.edu
SUMMARY:Multiplicities of graded families of ideals on Noetherian local rings
DESCRIPTION:Algebra Seminar \nSpeaker: Dale Cutkosky\, University of Missouri \nTitle: Multiplicities of graded families of ideals on Noetherian local rings \nAbstract: Let $R$ be an arbitrary $d$-dimensional Noetherian local ring with maximal ideal $m_R$. In this talk\, we give a generalization of the multiplicity $e(I)$ of an $m_R$-primary ideal $I$ of $R$ to a multiplicity $e(\mathcal I)$ of a graded family of $m_R$-primary ideals $\mathcal I$ in $R$. This multiplicity gives the classical multiplicity $e(I)$ if $\mathcal I=\{I^n\}$ is the $I$-adic filtration\, and agrees with the volume\, $\lim_{n\rightarrow \infty}d!\frac{\ell(R/I_n) }{n^d}$ for $R$ such that $\dim N(\hat R)>d$\, the required condition for the volume of graded families of $m_R$-primary ideals to exist as a limit. We will show that many of the classical theorems for the multiplicity of an ideal generalize to this multiplicity\, including mixed multiplicities\, the Rees theorem and the Minkowski inequality and equality. We give proofs which are independent of the theory of volumes and Okounkov bodies for all of our results\, with the one exception being the proof of the Minkowski equality. We do this by interpreting the multiplicity of graded families of $m_R$-primary ideals as an intersection product on the family of $R$-schemes which are obtained by blowing up $m_R$-primary ideals in $R$. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_4926/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-4.9.26.docx-scaled.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260416T160000
DTEND;TZID=America/New_York:20260416T170000
DTSTAMP:20260402T065852
CREATED:20260317T165726Z
LAST-MODIFIED:20260317T202152Z
UID:10003918-1776355200-1776358800@cmsa.fas.harvard.edu
SUMMARY:Interpolation for points in $\mathbb{P}^N\, N\geq 2$
DESCRIPTION:Algebra Seminar \nSpeaker: Dipendranath Mahato\, Tulane University \nTitle: Interpolation for points in $\mathbb{P}^N\, N\geq 2$ \nAbstract: Interpolation problems study hypersurfaces in projective space passing through prescribed sets of points. Classically\, one asks how many independent conditions a collection of points imposes on hypersurfaces of a fixed degree\, a question that can be studied algebraically via homogeneous ideals and their Hilbert functions. In this talk\, I will begin with the classical interpolation problem for reduced points and introduce the algebraic framework used to study it. I will then move to fat point schemes\, where points are assigned multiplicities and hypersurfaces are required to vanish to higher order. In this setting\, interpolation problems naturally lead to symbolic powers of ideals and containment relations between symbolic and ordinary powers. I will conclude by discussing open questions\, including potential connections between interpolation problems and combinatorial structures such as matroids.
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_41626/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-4.16.26.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260430T160000
DTEND;TZID=America/New_York:20260430T170000
DTSTAMP:20260402T065852
CREATED:20260302T145226Z
LAST-MODIFIED:20260330T200426Z
UID:10003913-1777564800-1777568400@cmsa.fas.harvard.edu
SUMMARY:Transcendental Epsilon Multiplicity via Divisor Volumes
DESCRIPTION:Algebra Seminar \nSpeaker: Sudipta Das\, Tata Institute of Fundamental Research \nTitle: Transcendental Epsilon Multiplicity via Divisor Volumes \nAbstract:  In this talk\, our goal is to establish a structural bridge between asymptotic commutative algebra and transcendence theory to show that there exists an ideal in a Noetherian local ring whose epsilon multiplicity is transcendental. By equating the local-cohomological definition of epsilon multiplicity to a global divisorial volume integral on a projective bundle\, we apply Baker’s theorem on linear forms in logarithms to prove that the resulting arithmetic invariant falls strictly outside the field of algebraic numbers. This talk is based on collaborative work with Vinh Pham and Stephen Landsittel. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_43026/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebra-Seminar-4.30.26.1-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260514T160000
DTEND;TZID=America/New_York:20260514T170000
DTSTAMP:20260402T065852
CREATED:20260330T154547Z
LAST-MODIFIED:20260330T154547Z
UID:10003926-1778774400-1778778000@cmsa.fas.harvard.edu
SUMMARY:Algebra Seminar
DESCRIPTION:Algebra Seminar \nSpeaker: Aryaman Maithani\, University of Utah \nTitle/Abstract: TBA
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_51426/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
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