Topology Seminars



Upcoming Topology Seminars
Past Topology Seminars
DMS Topology Seminar
Feb 28, 2024 01:00 PM
318 Parker Hall


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Speaker: Michel Smith (Auburn University)

Title: Non-metric Hereditarily Indecomposable Continua.

Abstract: The author discusses techniques for producing non-metric hereditarily indecomposable continua. Examples are presented.  However, attempts to generalize metric construction techniques yield situations in which hereditary indecomposability implies metrizability. We review the author's recent results regarding such situations.  Open problems in the area are stated.


DMS Topology Seminar
Feb 21, 2024 01:00 PM
318 Parker Hall


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Speakers: Michel Smith and Haley Pavlis (Haley Pavlis)

Abstract: We define the graph topology for finite graphs. We discuss the properties of a continuous map between graphs and properties of a traditional inverse limit of graphs. Most importantly, that a traditional inverse limit of finite path graphs is non-Hausdorff. We introduce a generalized inverse limit, where the first space is a metric arc and all other spaces are finite path graphs. Using the Bucket Handle continuum as an example, a technique is shown for constructing a generalized inverse limit, where the first space is a metric arc and the others are finite path graphs, that is homeomorphic to a traditional inverse limit of Hausdorff arcs.

Using crooked chains, we construct and analyze a non-Hausdorff hereditarily indecomposable continuum. This continuum has some interesting properties, which will be discussed. Ongoing research is discussed and open problems stated.(Michel Smith)

Title: Non-metric Hereditarily Indecomposable Continua.

Abstract: We discuss techniques for producing non-metric hereditarily indecomposable continua. Examples are presented.  However, attempts to generalize metric construction techniques yield situations in which hereditary indecomposability implies metrizability. We review our recent results regarding such situations.  Open problems in the area are stated.


DMS Topology Seminar
Feb 14, 2024 01:00 PM
318 Parker Hall


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Speaker: Hannah Alpert (Auburn University) Title: Unintuitive properties of Urysohn 1-width

Abstract: A metric space has small Urysohn 1-width if it admits a continuous map to a 1-dimensional complex where the preimage of each point has small diameter.  An open problem is, if a space's universal cover has small Urysohn 1-width, must the original space also have small Urysohn 1-width?  Naively, we would guess yes, but various strange examples suggest maybe not. 

 

Joint work with Panos Papasoglu, Arka Banerjee, Alexey Balitskiy, and Larry Guth.


DMS Topology Seminar
Apr 26, 2023 01:00 PM
ZOOM


Speaker: Vladimir Tkachuk (Universidad Autónoma Metropolitana de México) 

 

Title: On Lindelof scattered subspaces of nice \(sigma\)-products

Abstract: We will show that there exists an Eberlein compact space \(K\) such that some Lindelöf subspace of \(K\) fails to be a Lindelöf \(\Sigma\)-space. We also prove that any scattered Lindelöf subspace of a \(\sigma\)-product of first countable spaces is \(\sigma\)-compact. It is established that if \(X\) is the \(G_\delta\)-modification of a scattered compact space, then \(ext(C_p(X)) = \omega\).


DMS Topology Seminar
Mar 29, 2023 01:00 PM
224 Parker Hall


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Speaker: Ziqin Feng 

Title: On Vietoris-Rips Complex of Finite Metric SpacesAbstract: I will discuss the homotopy type of the Vietoris-Rips complex of finite metric spaces. These are related to the independent complex of the Kneser graphs and VR complex on hypercube graphs.


DMS Topology Seminar
Mar 01, 2023 01:00 PM
224 Parker Hall and ZOOM


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Speaker: Joseph Briggs Title: Infinitary DriskoAbstract: An elegant result from the 90's states that any filling of a 2𝑛 − 1 × 𝑛 array with distinct symbols in each column has a full transversal, namely a collection of 𝑛 cells from distinct rows and columns each with all entries distinct. The famous Ryser-Brualdi-Stein Conjecture from the 70’s suggests that for transversals of size 𝑛 − 1, such an 𝑛 × 𝑛 array suffices. This mysterious jump from 𝑛 to 2𝑛 − 1 columns remains elusive 30 years later, so we embark on a discussion of infinite variants in the hope of shedding some light.


DMS Topology Seminar
Feb 22, 2023 01:00 PM
224 Parker Hall


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Speaker: Brian Freidin Title: Free boundary minimal surfaces in the ballAbstract: Minimal surfaces are critical points for the area function on the space of submanifolds, say of R^n. In a bounded region V the free boundary problem asks for critical points of the area function on the space of submanifolds with boundary contained in the boundary of V. We will survey some results about what topologies can occur (classified by genus and number of boundary components in dimension 2) for free boundary minimal surfaces in the ball. Then we will discuss a construction for such surfaces by searching in the lower-dimensional space of G-invariant surfaces, for various groups G.


DMS Topology Seminar
Feb 15, 2023 01:00 PM
224 Parker Hall


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Speaker: Hannah Albert Title: Homology of configuration spaces of squares in a rectangleAbstract: We consider the configuration space of n unit squares sliding in a p by q rectangle.  In which degrees is its homology concentrated?  Squares in a rectangle serve as a model for molecules in a container.  Can we detect (approximately) whether the substance is a solid, liquid, or gas, using only the topology of the configuration space?  Even very basic questions about these configuration spaces tend to be unresolved, so there are many appealing directions for future research.


DMS Topology Seminar
Jan 27, 2023 01:00 PM
224 Parker Hall


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Speaker: Will Brian, University of North Carolina, Charlotte

 

Title: Large metric spaces and partitions of the real line into Borel setsAbstract: I will sketch a proof that, assuming $0^dagger$ does not exist, if there is a partition of $R$ into $ℵ_ω$ Borel sets, then there is also a partition of $R$ into $ℵ_{ω+1}$ Borel sets. (And the same is true for any singular cardinal of countable cofinality in place of $ℵ_ω$.) This contrasts starkly with the situation for cardinals with uncountable cofinality and their successors, where the spectrum of possible sizes of partitions of R into Borel sets can (via forcing) be made completely arbitrary. The proof of this fact for $ℵ_ω$ uses the structure of a certain complete metric space of weight $ℵ_ω$, and the existence of a particular partition of that space into Polish spaces.


DMS Topology Seminar
Jan 18, 2023 01:00 PM
224 Parker Hall


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Speaker: Arka Banerjee Title: Coarse cohomology of the complementAbstract: John Roe defined the notion of  Coarse cohomology of a metric space that measures the behavior at infinity of a space: more specifically, it measures the way in which uniformly large bounded sets fit together. In my talk I will give a brief introduction to this theory and define a new notion called "Coarse cohomology of the complement." Time permitting, I will discuss some related results and applications.

This talk is partly based on a joint work with Boris Okun.


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