## AWM Anniversary Conference at Brown University 2011

### Algebraic Geometry and Commutative Algebra I

• Organizers:
• Claudia Miller (Syracuse University)
• Mara Neusel (Texas Tech University)
• Janet Striuli (Fairfield University)

#### Resolutions over quadratic complete intersections

##### Irena Peeva, Cornell University

This talk is on the structure of the linear part of a minimal free resolution over a quadratic complete intersection.

#### Tensor complexes

##### Christine Berkesch, Duke University

I will discuss two examples where free resolutions appear in algebraic geometry, in the study of determinantal varieties and the construction of resultants for multilinear systems of equations. I will then
present a new construction for building multilinear free resolutions from tensors that simultaneously generalizes these examples. This is joint work with Daniel Erman, Manoj Kummini, and Steven Sam.

#### Cohomology over quasi-complete intersections

##### Ines Henriques, University of California at Riverside Adela Vraciu, University of South Carolina

We introduce and study a class of homomorphisms of commutative noetherian rings, which strictly contains the class of locally
complete intersection homomorphisms, while sharing many of its remarkable properties. This is joint work with L. Avramov and L. Sega.

#### The weak Lefscheftz property for monomial complete intersection ideals in positive characteristic

##### Adela Vraciu, University of South Carolina

We find explicit necessary and sufficient conditions for the ring k[x,y,z,w]/(x^d, y^d, z^d, w^d) to have the weak Lefschetz property when k is a field of positive characteristic. This is joint work with Andy Kustin.

### Conservation Laws — Analytical and Numerical Approaches I

• Organizers:
• Katarina Jegdic (University of Houston – Downtown)
• Barbara Keyfitz (The Ohio State University)

#### A kinetic equation for an elastic model, via a Hamiltonian lattice with two dimensional displacement field

##### Charis Tsikkou, Ohio State University

We work on a harmonic lattice with a nonquadratic on-site potential, and two dimensional displacement field, in the context of non linear elasticity. We use Wigner function, Gaussian decoupling and apply the kinetic theory of L. Boltzmann.

#### Weak transport theory and the vortex-wave system

##### Helena Nussenzveig Lopes, UNICAMP

The vortex-wave system is a coupling of the two-dimensional vorticity equation with the point-vortex system. It is a model for the motion of a finite number of concentrated vortices moving in a distributed vorticity background. In this talk we discuss existence of a weak solution to this system with an initial background vorticity in Lp, p > 2, up to the time of first collision of point vortices. We also discuss the existence of particle trajectories for this flow.

#### On the structure of solutions of nonlinear hyperbolic systems of conservation laws

##### Monica Torres, Purdue University

In this talk we show that a Liouville theorem for systems of conservation laws yields the existence of strong traces on hyperplanes of bounded solutions for the one dimensional isentropic Euler equations.

#### Global solutions for transonic self-similar 2-dimensional Riemann problems

##### Eun Heui Kim, California State University – Long Beach

We discuss the recent development of two-dimensional self-similar transonic Riemann problems. More precisely we discuss analytical results and numerical results on a simplified model system — the nonlinear wave system.

#### Strong regular reflection for two-dimensional isentropic gas dynamics equations

##### Katarina Jegdic, University of Houston, Downtown

We consider a Riemann problem for two-dimensional gas dynamics equations that gives rise to strong (or transonic) regular reflection. We write the problem in self-similar coordinates and we obtain a free boundary problem for the reflected shock and a subsonic state. We prove existence of a solution using various fixed point arguments and theory of second order elliptic equations with mixed boundary conditions.

### Cryptography I

#### On Probabilistic Proofs

##### Shafi Goldwasser, MIT

Abstract not available

#### Flavors and applications of verifiable random functions

##### Anna Lysyanskaya, Brown University

A random Boolean function is a function where for every input x, the value f(x) is truly random. A pseudorandom function is one where, even though f(x) can be deterministically computed from a small random “seed” s, no efficient algorithm can distinguish f from a random function upon querying it on inputs x1,…,xn of its choice. A verifiable random function (VRF) is a pseudorandom function that can be verified. That is to say, a VRF consists of four algorithms: Generate, Evaluate, Prove, Verify. Alice chooses uses Generate to pick her function f, Evaluate to evaluate it and compute y=f(x), Prove in order to compute a proof p(x) that y is indeed f(x). Bob can then use Verify in order to ascertain that it is indeed the case that y=f(x). At the same time, whenever Bob is not given a proof p(x) for a particular x, no efficient algorithm allows him to determine whether y=f(x) or is random. In this talk I will give a survey of verifiable random functions and their constructions and applications.

#### Elliptic Curve Primality Tests for Numbers in Special Forms

##### Alice Silverberg, University of California, Irvine

In joint work with Alex Abatzoglou and Angela Wong, we use elliptic curves with complex multiplication to give primality proofs for integers of certain forms,
generalizing earlier work of B. Gross and of R. Denomme and G. Savin who dealt with elliptic curves with complex multiplication by $Q(i)$ and $Q(\sqrt{-3})$.

#### Lattices in Cryptanalysis and List Decoding of Error-correcting Codes

Coppersmith’s algorithm is a celebrated technique for finding small solutions to polynomial equations modulo integers, and it has many important applications in cryptography. In this talk, I will show how to use lattices to recover an RSA private key from partial information and to find a large approximate common divisor of several integers. Then we will see how the ideas of this technique can be extended to a more general framework encompassing list decoding of Reed- Solomon, Parvaresh-Vardy, and algebraic-geometric codes. These seemingly different problems are all perfectly analogous when viewed from the perspective of algebraic number theory.

### Currents Trends in Probability

• Organizer:
• Kavita Ramanan (Brown University)

Abstracts not available

### Geometric Group Theory I

#### Hairy graphs and the cohomology of Out(F_n)

##### Karen Vogtmann, Cornell University

Kontsevich showed that the homology of Out(F_n) can be identified with the cohomology of a certain Lie algebra A. Morita constructed cocycles from elements of the abelianization of A. We will show that the abelianization of A is strictly larger than Morita conjectured, then use the new information to construct new cocycles out of “hairy graphs”. These include a heretofore mysterious unstable homology class in Aut(F_5) which was found in 2002 by F. Gerlits. (This is joint work with Jim Conant and Martin Kassabov.)

#### Instability in groups

##### Moon Duchin, Tufts University

In hyperbolic spaces, geodesics between the same endpoints must stay uniformly close together; this means that in hyperbolic groups, different geodesic spellings of the same word can’t be too far apart in the Cayley graph. In free abelian groups, on the other hand, typical words can have geodesic spellings quite far apart from one another because of the many ways to rearrange letters, even though the model spaces are Euclidean and geodesics there are unique.
We might describe this by staying that hyperbolic groups are geodesically stable while free abelian groups are geodesically unstable. I’ll focus this talk on an intermediate situation arising in the nilpotent case, where the groups break into a stable part and an unstable part.

#### Growth rate of an endomorphism of a group

##### Delaram Kahrobaei, City University of New York, Graduate Center and City Tech

Bowen defined the growth rate of an endomorphism of a finitely generated group and related it to the entropy of a map $f:M \mapsto M$ on a compact manifold. In this note we study the purely group theoretic aspects of the growth rate of an endomorphism of a finitely generated group. We show that it is finite and bounded by the maximum length of the image of a generator. An equivalent formulation is given that ties the growth rate of an endomorphism to an increasing chain of subgroups. We then consider the relationship between growth rate of an endomorphism on a whole group and the growth rate restricted to a subgroup or considered on a quotient.We use these results to compute the growth rates on direct and semidirect products. We then calculate the growth rate of endomorphisms on several different classes of groups including abelian and nilpotent. This is a joint work with Kenneth Falconer and Benjamin Fine.

### Group Theory and Its Connections to Representation Theory I

• Organizers:
• Terrell Hodge (Western Michigan University)
• Julianne Rainbolt (St. Louis University)

Abstracts not available

### Homotopy Theory and Its Applications I

#### Algebraic Structures from diagrams

##### Julie Bergner, University of California, Riverside

We investigate ways to understand various algebraic structures via diagrams satisfying a Segal-type condition. Such diagrams have been used extensively for monoid or category structures in models for (\infty,1)-categories, but here we look at ways to understand other kinds of algebraic objects. This project is joint work with Philip Hackney.

#### The S^1 equivariant generating hypothesis

##### Anna Marie Bohmann, Northwestern University

Freyd’s generating hypothesis is a long-standing conjecture in stable homotopy theory, which says that the stable homotopy groups functor is faithful on finite spectra. We give the appropriate generalization to the equivariant context, where we prove that for finite groups of equivariance, the situation is similar to the nonequivariant case. For circle actions, the picture is strikingly different: even the rational S^1 equivariant generating hypothesis fails.

#### Spectral sequences of operad algebras

##### Kristine Bauer, University of Calgary

Since the 1950’s, topologists have understood how to use the multiplicative structure of a spectral sequence of algebras to aid in the study of the spectral sequence. In good cases, such a spectral sequence converges as an algebra, so that the $E^\infty$ page again has multiplicative structure. In this talk, we explain what it means for a spectral sequence to be a sequence of operad algebras. We give conditions which ensure that the sequence converges as
operad algebras and look at examples of how this can be useful in detecting certain (co)homological operations. This is joint work with Laura Scull.

#### Coincidence invariants

##### Kate Ponto, University of Kentucky

A fixed point of a continuous endomorphism f of a topological space
X is a point x in X so that f(x)=x. A coincidence point of a pair of continuous maps f and g from X to Y is a point x in X so that f(x)=g(x). Coincidence points are a natural generalization of fixed points. I will explain how the formal structure that describes the Lefschetz fixed point theorem also describes a corresponding theorem for (some) coincidence invariants.

### Intersection of Mathematics and Mathematics Education: Research and Practice K-20

• Organizers:
• Juliana Belding (Harvard University)
• Ginger Warfield (University of Washington)

#### Research in Mathematics Education: Looking Back and Looking Forward

##### Karen Graham, University of New Hampshire

Abstract: This talk will provide an overview of research in mathematics education K-20 over the last 40 years; the major themes and methodologies that have shaped the research and informed practice. We will also look forward to what might be important focus areas in the future.

#### A Mathematics Education Researcher’s Travels: Perspectives on Mathematics Education Research from Academia, Government, and Professional Societies

##### Karen King, New York University

Abstract: In this talk, I describe my perspective on research in mathematics education, its past and future, through my travels as a faculty member in departments of teacher education and mathematics across the country, a program officer at the National Science Foundation and now the Director of Research at the National Council of Teachers of Mathematics. Through the lens of my various experiences, I will present one perspective on the future of mathematics education research PK-20 and the role of mathematicians and mathematics educators in that future.

#### Helping Students with Proving: A Tale of Two Whole Class Teaching Experiments

##### Annie Selden, New Mexico State University

First, I will discuss a whole class teaching experiment for helping advanced undergraduate and beginning graduate mathematics students construct proofs. This course has been taught seven times since Fall 2007 and each time we are learning something more about students’ proving capabilities. For example, there are certain aspects of proving that mathematicians do automatically, but that students are often unaware of. We define the formal-rhetorical part of a proof to be those aspects of a proof that can be written by examining the logical structure of the statement of a theorem and by unpacking associated definitions.
Examples include writing the first and last lines, “unpacking” the meaning of the last line, and considering what strategy one might invoke to prove that. Writing the formal-rhetorical part of a proof can expose “the real problem(s)” to be solved. We call the remainder of the proof the problem-centered part.
Second, I will discuss a voluntary proving supplement for an undergraduate real analysis class. This has been taught three times to since Fall 2009. Each week, one proof problem was selected or created to “resemble in construction” an assigned homework proof problem that the real analysis teacher intended to grade in detail, and that could be improved subsequently and resubmitted
for additional credit. The supplement proof problem could be solved using actions similar to those useful in proving the corresponding assigned homework proof problem. However, the supplement proof problem was not a template problem, and “on the surface” would often not resemble the assigned proof problem.
The teaching for both the proofs course and the supplement has been informed by our theory of actions in the proving process and by our division of proofs into their formal-rhetorical and problem-centered parts.

#### TITLE not available

##### Natasha Speer, University of Maine

ABSTRACT not available

### Mathematical Biology — An Overview

• Organizers:
• Holly Gaff (Old Dominion University)
• Maeve L. McCarthy (Murray State University)

Abstracts not available

### Recent Advances in Numerical Methods and Scientific Computing I

• Organizers:
• Sigal Gottlieb (University of Massachusetts-Dartmouth)
• Misha Kilmer (Tufts University)

#### Accelerated Fixed Point Methods for Subsurface Flow Problems

##### Carol Woodward, LLNL

We investigate effectiveness of an acceleration method applied to the modified Picard iteration for simulations of variably saturated flow. We solve nonlinear systems using both unaccelerated and accelerated modified Picard iteration as well as Newton’s method. Since Picard iterations can be slow to converge, the advantage of acceleration is to provide faster convergence while maintaining advantages of the Picard method over the Newton method. Results indicate that the accelerated method provides a robust solver with significant potential computational advantages.
Authors: P. A. Lott, H. F. Walker, C. S. Woodward, and U. M. Yang

#### Block Preconditioners for Coupled Fluid Problems

##### Victoria Howle, Texas Tech

Many important engineering and scientific systems require the solution of extensions to standard incompressible flow models, whether by coupling to other processes or by incorporating additional nonlinear effects. Finite element methods and other numerical techniques provide effective discretizations of these systems, and the generation of the resulting algebraic systems may be automated by high-level software tools such those in the Sundance project, but the efficient solution of these algebraic equations remains an important challenge.
Frequently, the nonlinear equations are linearized by a fixed point or Newton technique, and then the linear systems are solved by a preconditioned Krylov method such as GMRES. In this talk, we discuss important extensions to the methodology and analysis of preconditioning such systems. In particular, we extend existing block-structured preconditioners (such as those of Elman, et al.) to address some of these coupled systems, showing how an effective preconditioner for Navier-Stokes may be combined with one for some other process such as convection-diffusion of temperature to obtain a preconditioner for the Newton linearization of a nonlinearly coupled system such as Bénard convection.

#### Tensor factorizations in image processing

##### Misha Kilmer, Tufts University

Consider a collection of two-dimensional images. This set can be stored as a third order tensor (multi-way array). In this talk, we investigate the use of new tensor factorizations as a sum of k, product cyclic tensors, that are suitable for compression of such
multiway data, and which can be tuned to preserve features such as non-negativity.

#### Order-p Tensors: Factoring and Applications

##### Carla D. Martin, James Madison University

Tensor decompositions or representations of multiway arranys have been motivated by applications. Given that data is often multidimensional, extending powerful linear algebra concepts to tensors has been crucial for interpretation of the data as well as data compression. In this talk, we describe a factorization that is SVD-like in nature, for general order-p tensors. The idea is best explained using recursive programming, but is implemented directly using the fast Fourier transform. In particular, we present an alternative representation for order-p tensors as a ‘product’ of tensors which is reminiscent of the matrix factorization approach. This leads to a different generalization of the matrix SVD. Furthermore, our framework allowed other matrix factorizations to be extended to tensors. We also present algorithms for computation and potential applications.

### Symplectic and Contact Geometry I

• Organizers:
• Eleny Ionel (Stanford University)
• Katrin Wehrheim (MIT)

#### 11:15 Conley conjecture for negative monotone symplectic manifolds

##### Basak Gurel, Vanderbilt

The Conley conjecture, formulated by Conley in 1984, asserts the existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms of tori and was established by Hingston in 2004. Of course, one can expect the conjecture to hold for a much broader class of closed manifolds and this is indeed the case. For instance, by now, it has been proved for all closed, symplectically aspherical manifolds and Calabi-Yau manifolds using symplectic topological methods. Most recently, jointly with Ginzburg, we establish the conjecture for negative monotone, closed symplectic manifolds.
In this talk, we will briefly examine the question of existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms and outline a proof of the Conley conjecture in the negative monotone case.

#### 11:45 Quilts and Floer modules

##### Sikimeti Ma’u, UC Berkeley

I’ll describe some general A-infinity module structure that appears in Quilted Floer theory. This structure lies behind spectral sequences on hypercuboid complexes encoding relationships between different Quilted Floer homology groups. I’ll illustrate with examples based on compositions of Dehn twists.

### Advances in Nonlinear Dynamics I

• Organizers:
• Alethea Barbaro (UCLA)
• Andrea Bertozzi (UCLA)

#### Spatio-temporal feedback control of unstable wave patterns

##### Mary Silber, Northwestern University

We extend the methods of Pyragas time-delayed feedback control of unstable periodic orbits to the situation where the unstable periodic orbits arise in a symmetry breaking Hopf bifurcation. We consider traveling wave patterns with spatio-temporal symmetries, as well as oscillator patterns
for equivariant Hopf bifurcation problems.

#### TITLE not available

##### Nancy Rodriguez, Stanford University

ABSTRACT not available

#### An evolving network model for gang rivalries in Los Angeles

##### Alethea Barbaro, UCLA

Gang rivalries is a leading cause of violent crime in many cities. However, there is still much to be understood about how and why these rivalries form. We introduce an agent-based model coupled to an evolving network in order to explore how such rivalries might arise.

#### TITLE not available

##### Brittany Erickson, Stanford University

ABSTRACT not available

### Algebraic Geometry and Commutative Algebra II

• Organizers:
• Claudia Miller (Syracuse University)
• Mara Neusel (Texas Tech University)
• Janet Striuli (Fairfield University)

#### Hypergeometric functions and toric varieties

##### Laura Matusevich, Texas A&M University

I will discuss structural issues relating to the classical
hypergeometric equations of Horn type. The key idea (due to Gelfand,
Graev, Kapranov and Zelevinsky) is to construct torus equivariant
versions of these differential equations and study them using D-module theoretic techniques. Transferring results back to the original setting has proved challenging. I will report on recent progress in this direction, joint with Christine Berkesch.

#### Spaces of rational curves on hypersurfaces

##### Roya Beheshti Zavareh, Washington University in St. Louis

I will discuss some aspects of the geometry of spaces of rational
curves on general Fano hypersurfaces including dimension,
irreducibility, and birational geometry. A part of this talk is based on joint work with Mohan Kumar.

#### Conformal blocks and the Mori dream space conjecture

##### Angela Gibney, University of Georgia at Athens

Given a simple Lie algebra, a positive integer, and an appropriately chosen n-tuple of dominant integral weights, one can define a vector bundle on the moduli space of curves whose fibers are the so-called vector spaces of conformal blocks. On moduli spaces of pointed rational curves, first Chern classes of these vector bundles turn out to be semi-ample divisors, and so define morphisms. In this talk I will discuss the simplest examples of these divisors, and discuss how they relate to a big-picture conjecture of Hu and Keel about the birational geometry of the moduli space.

#### Arrangements of Lines: Syzygies and secants

##### Jessica Sidman, Mount Holyoke College

We discuss arrangements of lines that are curves of genus g embedded in projective space. We produce embeddings whose ideals are generated by products of linear forms. We also discuss the syzygies of these line arrangements as well as the syzygies of their secant varieties.

### Combinatorics and Graph Theory I

• Organizers:
• Ruth Haas (Smith College)
• Ann Trenk (Wellesley College)

#### Some problems on list-coloring planar graphs/h4>

##### Joan P. Hutchinson, Macalester College

A graph G is said to be L-list-colorable when each vertex v is assigned a list L(v) of colors and G can be properly colored so that each v receives a color from L(v). Typically the lists L may vary from vertex to vertex. A graph is said to be k-list- colorable when it can be L-list-colored whenever every list L(v) contains at least k colors. A celebrated theorem of C. Thomassen proves that every planar graph can be 5-list-colored. An unresolved question of M.O. Albertson asks whether there is a distance d > 0 such that whenever a set P of vertices of a planar graph G are precolored and are mutually at distance at least d from one another, the precoloring extends to a 5-list-coloring of G. In this talk we give some partial affirmative answers to Albertson’s question and investigate the extent to which Thomassen’s theorem and Albertson’s question are best possible. This talk includes joint work with co-authors Maria Axenovich, Alice M. Dean, and Michelle A. Lastrina.

#### Ribbon graphs and twisted duality

##### Jo Ellis-Monaghan, St. Michael’s College

Abstract: We consider two operations on the edge of an embedded (or ribbon) graph: giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of ${S_3}^{e(G)}$, the ribbon group of $G$, on $G$. We show that this ribbon group action gives a complete characterization of duality in that if $G$ is any cellularly embedded graph with medial graph $G_m$, then the orbit of $G$ under the group action is precisely the set of all graphs with medial graphs isomorphic (as abstract graphs) to $G_m$. We then show how this group action leads to a deeper understanding of the properties of, and relationships among, various graph polynomials, Petrie duals, and some knot and link invariants. This is joint work with Iain Moffatt.

#### On generalized configurations

##### Brigitte Servatius, WPI

Abstract: We consider generalized configurations as defined by Konrad Zindler (1890) and study their degree of irregularity and their automorphism group. We give a construction of a family of such configurations of arbitrarily large degree of irregularity. This is joint work with Tomaz Pisanski.

#### Symmetry Breaking in Matroids

##### Speaker: Jenny McNulty, The University of Montana

Abstract: What can we do to an object to break its symmetry?” That is, how can we restrict the object in some way so that the only automorphism is trivial? We examine two approaches. The first involves distinguishing the elements of the object while the second involves fixing some of the elements. Distinguishing and fixing numbers were originally defined for graphs. We are interested in the extension of these ideas to matroids. We give a sampling of fixing and distinguishing number results for matroids.

### Geometric Group Theory II

#### Length functions of right-angled Artin groups

##### Ruth Charney, Brandeis University

Morgan and Culler proved that a minimal action of a free group on a tree is determined by its length function. This theorem has played an important role in the study of automorphism groups of free groups. Right-angled Artin groups may be viewed as higher dimensional analogues of free groups. Motivated by an interest in their automorphism groups, we prove a 2-dimensional analogue of Culler and Morgan’’s theorem for right-angled Artin groups acting on CAT(0) rectangle complexes. (Joint work with Max Margolis)

#### The geometry of right-angled Artin subgroups of mapping class groups

##### Johanna Mangahas, Brown University

I’ll describe joint work with Matt Clay and Chris Leininger. We give sufficient conditions for a finite set of mapping classes to generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmueller space is a quasi-isometric embedding for both of the standard metrics. As a consequence, we produce infinitely many genus h surfaces (h at least 2) in the moduli space of genus g surfaces (g at least 3) for which the universal covers are quasi-isometrically embedded in the Teichmueller space.

#### L-functions and periods

##### Brooke Feigon, University of East Anglia

I will describe recent work relating L-functions to periods.

ABSTRACT

ABSTRACT

ABSTRACT

ABSTRACT

ABSTRACT

### Symplectic and Contact Geometry II

#### 8:30 Contact Invariant in Sutured Floer Homology

##### Gordana Matic, University of Georgia

We describe an invariant of contact structures in Sutured Floer Homology and show some applications to non-fillability of contact structures. This is joint work with Ko Honda and Will Kazez.

#### 9:00 Transverse invariants in Heegaard Floer homology

##### Vera Vertesi, MIT

Using the language of Heegaard Floer knot homology recently two invariants were defined for Legendrian knots. One in the standard contact 3-sphere defined by Ozsvath, Szabo and Thurston in the combinatorial settings of knot Floer homology, one by Lisca, Ozsvath, Stipsicz and Szabo in knot Floer homology for a general contact 3–manifold. Both of them naturally generalizes to transverse knots. In this talk I will give a characterization of the transverse invariant, similar to the one given by Ozsvath and Szabo for the contact invariant. Namely for transverse braids both transverse invariants are given as the bottommost elements with respect to the filtration of knot Floer homology given by the axis. The above characterization allows us to prove that the two invariants are the same in the standard contact 3–sphere. This is a joint work with J. Baldwin and D.S. Vela-Vick.

#### 9:30 Legendrian Contact Homology in Seifert Fibered Spaces

##### Joan Licata, Stanford University

Seifert fibered spaces can be viewed as circle bundles over surface orbifolds. We consider when these manifolds can be equipped with contact forms whose Reeb orbits realize the Seifert fibers, and we construct a combinatorial invariant modeled on Legendrian contact homology for Legendrian knots in these contact manifolds. This is joint work with J. Sabloff.

#### 10:00 Topological Invariants of Orbifolds

##### Tara Holm, Cornell

We present techniques for computing the various cohomology and K-theory rings associated to an orbifold X that arises as a symplectic quotient M//G. We will pay particular attention to the example of a weighted projective space, where many computations simplify.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8908517,"math_prob":0.80678666,"size":72299,"snap":"2023-40-2023-50","text_gpt3_token_len":15488,"char_repetition_ratio":0.13584618,"word_repetition_ratio":0.03203724,"special_character_ratio":0.18268579,"punctuation_ratio":0.08439127,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9673556,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-02T03:53:58Z\",\"WARC-Record-ID\":\"<urn:uuid:36c1114f-e63d-4fd6-bd82-bc06d3f88e96>\",\"Content-Length\":\"242298\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d73a1a7d-4433-4e5d-9ef9-0b0e9d87b54c>\",\"WARC-Concurrent-To\":\"<urn:uuid:fe0a786f-db14-4074-b45e-dc7ddca47faa>\",\"WARC-IP-Address\":\"35.212.108.173\",\"WARC-Target-URI\":\"https://awm-math.org/meetings/awm-research-symposium/awm-anniversary-conference-2011/awm-anniversary-conference-2011-special-session-abstracts/\",\"WARC-Payload-Digest\":\"sha1:ORM4CISN5MC7XALVJPHNHRTBBK3FSLHC\",\"WARC-Block-Digest\":\"sha1:EOTIFCCITCUON5KJU64KE4XGLLY5AZIM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510967.73_warc_CC-MAIN-20231002033129-20231002063129-00344.warc.gz\"}"}