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TEXT

American Mathematical Society :: Homepage

American Mathematical Society :: Homepage

The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and ot

Advancing Research. Creating Connections.

The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.

Join us today »

From Notices of the AMS

A Fruitful Interaction Between Algebra, Geometry, and Topology: Varieties through the Lens of Group Actions

by Rubí E. Rodríguez
Anita M. Rojas
Communicated by Han-Bom Moon

Beautiful theories have emerged from mixing different areas of mathematics, when building bridges between areas provides the right paths to achieve the comprehension of a certain subject. Mathematicians know that if an object has several underlying structures, then the answer to some question considering one aspect of the object may come from another aspect of itself. A remarkable example of this is Descartes's use of coordinates; this milestone was the key to translate questions from geometry to algebra. But there are many other examples: Galois theory, algebraic geometry, mathematical physics, and the list goes on and on.

In these notes we will discuss how the knowledge about group algebras and representation theory has proved fruitful in understanding fundamental questions about complex abelian varieties, compact Riemann surfaces, and their moduli spaces.

Let us begin by roughly introducing these objects. Abelian varieties and compact Riemann surfaces are complex manifolds; that is, (connected, Hausdorff) topological spaces that locally look like open subsets of $\mathbbC

Figure 1---and that also share the property of being varieties.

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        <span itemprop="name">University of Texas</span>
</span>
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        <span itemprop="name">Georgia Southern University</span>
</span>
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University<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">University</span>
</span>
at Albany, Albany, NY

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University of California<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">University of California</span>
</span>
, Riverside, CA

Joint International Meeting of the AMS, NZMS, and AustMS

Joint meeting of New Zealand, Australian and American Mathematical Societies. University of Auckland<span itemscope itemtype="http://schema.org/Organization">
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, Auckland, New Zealand

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</span>
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University of Kansas<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">University of Kansas</span>
</span>
, Lawrence, KS

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University of Connecticut<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">University of Connecticut</span>
</span>
at Convention Center<span itemscope itemtype="http://schema.org/Organization">
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</span>
and Marriott, Hartford, CT

Spring Western Sectional Meeting

California State Polytechnic University<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">California State Polytechnic University</span>
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, San Luis Obispo<span itemscope itemtype="http://schema.org/Person">
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</span>
, CA

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2024 Fall Central Sectional - Abstract Submissions

Sep 14-15, University of Texas<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">University of Texas</span>
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, San Antonio

2024 Fall Central Sectional - Child Care Grants

Sep 14-15, University of Texas<span itemscope itemtype="http://schema.org/Organization">
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</span>
, San Antonio

Graduate Student Travel Grant Applications to 2024 Fall Sectional Meetings

Sep 14-15, University of Texas<span itemscope itemtype="http://schema.org/Organization">
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2024 Fall Southeastern Sectional - Abstract Submissions

Oct 5-6, Georgia Southern University<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">Georgia Southern University</span>
</span>
, Savannah, GA

2024 Fall Southeastern Sectional - Child Care Grants

Oct 5-6, Georgia Southern University<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">Georgia Southern University</span>
</span>
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2025 Spring Southeastern Sectional - Special Session Proposals

March 8-9, 2025, Clemson University<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">Clemson University</span>
</span>
, Clemson, SC

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Oct 19-20, University of Albany<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">University of Albany</span>
</span>
, NY

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Oct 19-20, University of Albany<span itemscope itemtype="http://schema.org/Organization">
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, NY

2025 Spring Central Sectional - Special Session Proposals

Mar 29-30, 2025. University of Kansas<span itemscope itemtype="http://schema.org/Organization">
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, Lawrence, KS

2024 Fall Western Sectional - Abstract Deadline

Oct 26-27, University of California<span itemscope itemtype="http://schema.org/Organization">
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, Riverside

2024 Fall Western Sectional - Child Care Grants

Oct 26-27, University of California<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">University of California</span>
</span>
, Riverside

JPBM Communications Award - Nominations

Joint Policy Board<span itemscope itemtype="http://schema.org/Organization">
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</span>
for Mathematics

2025 Spring Eastern Sectional - Special Session Proposals

Apr 5-6, 2025. University of Connecticut<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">University of Connecticut</span>
</span>
at Convention Center<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">Convention Center</span>
</span>
and Marriott, Hartford, CT

2025 Spring Western Sectional - Special Session Proposals

May 3-4, 2025, California Polytechnic State University<span itemscope itemtype="http://schema.org/Organization">
        <span itemprop="name">California Polytechnic State University</span>
</span>
, San Luis Obispo<span itemscope itemtype="http://schema.org/Person">
        <span itemprop="name">Luis Obispo</span>
</span>
, CA

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Jan 8-11, Seattle, Washington

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